Q. 5.29 - Intermediate Algebra

Question

Simplify each expression:

$ⓐ z^{-3} ⓑ {10}^{-7} ⓒ \frac{1}{p^{-8}} ⓓ \frac{1}{ 4^{-3}}$

Step-by-Step Solution

Answer

The simplified expression of $z^{-3}=\frac{1}{z^3}$

The simplified expression of ${10}^{-7}=\frac{1}{ {10}^7}$

The simplified expression of $\frac{1}{p^{-8}}=p^8$

The simplified expression of $\frac{1}{4^{-3}}=64$

Step 1. Given Information

In the given question we have to simplify each expression:

$ⓐ z^{-3} ⓑ {10}^{-7} ⓒ \frac{1}{p^{-8}} ⓓ \frac{1}{ 4^{-3}}$

Part (a) Step 1. The given expression is z − 3  

Using the definition of a negative exponent, $a^{-n}=\frac{1}{a^n}$

$z^{-3}=\frac{1}{z^3}$

Part (b) Step 1. The given expression is   10 − 7

Using the definition of a negative exponent, $a^{-n}=\frac{1}{a^n}$

${10}^{-7}=\frac{1}{ {10}^7}$

Part (c) Step 1. The given expression is 1 p − 8

Using the definition of a negative exponent, $\frac{1}{a^n}=a^{-n}$

$\frac{1}{p^{-8}}=p^8$

Part (d) Step 1. The given expression is 1 4 − 3

Using the definition of a negative exponent, $\frac{1}{a^n}=a^{-n}$

$$\begin{gathered} \frac{1}{4^{-3}}=4^3 \\ \frac{1}{4^{-3}}=64 \end{gathered}$$