In Exercises 1 and 2, use the properties of exponents to simplify. 1. a. x 4 · x 3 b. x 12 x 7 c. (4 ay ) 4 d. ( 3 4 ) 4 e. 2 3 · 2 2 f. ( x 4 ) 2

Question

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Answer 1

Textbook Question

Chapter 5, Problem 1TE

In Exercises 1 and 2, use the properties of exponents to simplify.

1.

a. x⁴ · x³
b. $x 12 x 7$
c. (4ay)⁴
d. $( 3 4 ) 4$
e. 2³ · 2²
f. (x⁴)²

a.

Expert Solution

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

b.

Expert Solution

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

c.

Expert Solution

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

d.

Expert Solution

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

e.

Expert Solution

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

f.

Expert Solution

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

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Answer 2

Textbook Question

Chapter 5, Problem 1TE

In Exercises 1 and 2, use the properties of exponents to simplify.

1.

a. x⁴ · x³
b. $x 12 x 7$
c. (4ay)⁴
d. $( 3 4 ) 4$
e. 2³ · 2²
f. (x⁴)²

a.

Expert Solution

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

b.

Expert Solution

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

c.

Expert Solution

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

d.

Expert Solution

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

e.

Expert Solution

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

f.

Expert Solution

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

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Answer 3

Textbook Question

Chapter 5, Problem 1TE

In Exercises 1 and 2, use the properties of exponents to simplify.

1.

a. x⁴ · x³
b. $x 12 x 7$
c. (4ay)⁴
d. $( 3 4 ) 4$
e. 2³ · 2²
f. (x⁴)²

a.

Expert Solution

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

b.

Expert Solution

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

c.

Expert Solution

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

d.

Expert Solution

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

e.

Expert Solution

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

f.

Expert Solution

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 5, Problem 1TE

In Exercises 1 and 2, use the properties of exponents to simplify.

1.

a. x⁴ · x³
b. $x 12 x 7$
c. (4ay)⁴
d. $( 3 4 ) 4$
e. 2³ · 2²
f. (x⁴)²

a.

Expert Solution

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

b.

Expert Solution

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

c.

Expert Solution

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

d.

Expert Solution

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

e.

Expert Solution

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

f.

Expert Solution

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

b.

Expert Solution

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

c.

Expert Solution

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

d.

Expert Solution

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

e.

Expert Solution

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

f.

Expert Solution

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

Answer 8

a.

Expert Solution

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To simplify: The expression $x4⋅x3$ by using the properties of exponents.

Answer 13

Answer to Problem 1TE

The simplified form of $x4⋅x3$ is $x7$ .

Answer 14

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $x4⋅x3$ .

Here, $a=x$ , $m=4$ and $n=3$ .

Use product property and simplify the expression as follows.

$x4⋅x3=x4+3=x7$

Therefore, the simplified form of $x4⋅x3$ is $x7$ .

Answer 15

b.

Expert Solution

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To simplify: The expression $x12x7$ by using the properties of exponents.

Answer 20

Answer to Problem 1TE

The simplified form of $x12x7$ is $x5$ .

Answer 21

Explanation of Solution

Formula used:

Quotient property:

For real number a and integers m and n, the quotient property is $aman=am−n,a≠0$ .

Calculation:

The given expression is $x12x7$ .

Here, $a=x$ , $m=12$ and $n=7$ .

Use quotient property and simplify the expression as follows.

$x12x7=x12−7=x5$

Therefore, the simplified form of $x12x7$ is $x5$ .

Answer 22

c.

Expert Solution

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

To simplify: The expression $(4ay)4$ by using the properties of exponents.

Answer 27

Answer to Problem 1TE

The simplified form of $(4ay)4$ is $256a4y4$ .

Answer 28

Explanation of Solution

Formula used:

Power of a product property:

For real numbers a and b and integers m and n, the power of product property is $(ab)m=ambm$ .

Calculation:

The given expression is $(4ay)4$ .

Here, $a=4a$ , $b=y$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(4ay)4=(4a)4(y)4=256a4y4$

Therefore, the simplified form of $(4ay)4$ is $256a4y4$ .

Answer 29

d.

Expert Solution

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

To simplify: The expression $(3z)4$ by using the properties of exponents.

Answer 34

Answer to Problem 1TE

The simplified form of $(3z)4$ is $34z4$ .

Answer 35

Explanation of Solution

Formula used:

Power of a Quotient property:

For real numbers a and b and integers m and n, the power of Quotient property is $(ab)m=ambm, for b≠0$ .

Calculation:

The given expression is $(3z)4$ .

Here, $a=3$ , $b=z$ and $m=4$ .

Use the above property and simplify the expression as follows.

$(3z)4=34z4=81z4$

Therefore, the simplified form of $(3z)4$ is $81z4$ .

Answer 36

e.

Expert Solution

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

Answer 37

e.

Expert Solution

Answer 38

e.

Expert Solution

Answer 39

Expert Solution

Answer 40

To determine

To simplify: The expression $23⋅22$ by the using properties of exponents.

Answer 41

Answer to Problem 1TE

The simplified form of $23⋅22$ is 32.

Answer 42

Explanation of Solution

Formula used:

Product property:

For real number a and integers m and n, the product property is $am⋅an=am+n$ .

Calculation:

The given expression is $23⋅22$ .

Here, $a=2$ , $m=3$ and $n=2$ .

Use the product property and simplify the expression as follows.

$23⋅22=23+2=25=32$

Therefore, the simplified form of $23⋅22$ is 32.

Answer 43

f.

Expert Solution

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

Answer 44

f.

Expert Solution

Answer 45

f.

Expert Solution

Answer 46

Expert Solution

Answer 47

To determine

To simplify: The expression $(x4)2$ by using the properties of exponents.

Answer 48

Answer to Problem 1TE

The simplified form of $(x4)2$ is $x8$ .

Answer 49

Explanation of Solution

Formula used:

Power of a power property:

For real number a and integers m and n, the power of a power property is $(am)n=amn$ .

Calculation:

The given expression is $(x4)2$ .

Note that here, $a=x$ , $m=4 and n=2$ .

Use the above property and simplify the expression as follows.

$(x4)2=x4⋅2=x8$

Therefore, the simplified form of $(x4)2$ is $x8$ .

Answer 50

Ch. 5.1 - Which of the following functions are exponential...Ch. 5.1 - Prob. 2E Ch. 5.1 - a. Graph the function f(x) = ex on the window [5,...Ch. 5.1 - a. Graph the function f(x) = 5x on the window [5,...Ch. 5.1 - Graph the function y = 3x on [5, 5] by [10, 30].Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

In Exercises 1 and 2, use the properties of exponents to simplify. 1. a. x 4 · x 3 b. x 12 x 7 c. (4 ay ) 4 d. ( 3 4 ) 4 e. 2 3 · 2 2 f. ( x 4 ) 2

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