Question

Simplify each expression:

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

Short 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-by-step solution

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 1p−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 14−3

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

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