Chapter 7.2, Problem 1P

a.

To determine

To Write: The expression $8^3\cdot 8^6$ using each base only once.

Answer to Problem 1P

The required answer is $8^9$ .

Explanation of Solution

Given information:

The expression $8^3\cdot 8^6$

Calculation:

  $\begin{array}{l}{8}^3\cdot 8^6\\ =8^{3+6}\end{array}$

(Add the exponents of the powers with the same base)

  $=8^9$

(Simplify the exponent)

b.

To determine

To Write: The expression ${\left(0.5\right)}^{-3}{\left(0.5\right)}^{-8}$ using each base only once.

Answer to Problem 1P

The required answer is ${\left(0.5\right)}^{-11}$ .

Explanation of Solution

Given information:

The expression ${\left(0.5\right)}^{-3}{\left(0.5\right)}^{-8}$

Calculation:

  $\begin{array}{l}{\left(0.5\right)}^{-3}{\left(0.5\right)}^{-8}\\ ={\left(0.5\right)}^{-3+\left(-8\right)}\end{array}$

(Add the exponents of the powers with the same base)

  $={\left(0.5\right)}^{-11}$

(Simplify the exponent)

c.

To determine

To Write: The expression $9^{-3}\cdot 9^2\cdot 9^6$ using each base only once.

Answer to Problem 1P

The required answer is $9^5$ .

Explanation of Solution

Given information:

  $9^{-3}\cdot 9^2\cdot 9^6$

Calculation:

  $\begin{array}{l}{9}^{-3}\cdot 9^2\cdot 9^6\\ =9^{-3+2+6}\end{array}$

(Add the exponents of the powers with the same base)

  $=9^5$

(Simplify the exponent)