Chapter 7.1, Problem 1P

a.

To determine

To Simplify: The expression $4^{-3}$

Answer to Problem 1P

The required answer is: $\frac{1}{64}$

Explanation of Solution

Given information:

The expression $4^{-3}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $4^{-3}$

(Applying negative exponent concept)

  $=\frac{1}{4^3}$

(Simplify)

  $=\frac{1}{64}$

b

To determine

To Simplify: The expression $-5^0$

Answer to Problem 1P

The required answer is: $n^3$

Explanation of Solution

Given information:

The expression $-5^0$

Concept Used:

Zero as an Exponent:

  $a^0=1$

Where a is a non-zero number.

Calculation:

  $-5^0$

(Applying Zero as an Exponent Concept)

  $=1$

c

To determine

To Simplify: The expression $3^{-2}$ .

Answer to Problem 1P

The required answer is: $\frac{1}{9}$

Explanation of Solution

Given information:

The expression $3^{-2}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $3^{-2}$

(Applying Negative Exponent Concept)

  $=\frac{1}{3^2}$

Simplify

  $=\frac{1}{9}$

d

To determine

To Simplify: The expression $6^{-1}$ .

Answer to Problem 1P

The required answer is: $\frac{1}{6}$

Explanation of Solution

Given information:

The expression $6^{-1}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  $6^{-1}$

(Applying Negative Exponent Concept)

  $=\frac{1}{6}$

e

To determine

To Simplify: The expression ${\left(-4\right)}^{-2}$

Answer to Problem 1P

The required answer is: $\frac{1}{16}$

Explanation of Solution

Given information:

The expression ${\left(-4\right)}^{-2}$

Concept Used:

Negative Exponent:

  $a^{-n}=\frac{1}{a^n}$

Where a is a non-zero number and n is an integer

Calculation:

  ${\left(-4\right)}^{-2}$

(Applying Negative Exponent Concept)

  $\begin{array}{l}=\frac{1}{-4^2}\\ =\frac{1}{16}\end{array}$