Question

Simplify each expression:

$ⓐn^{-2}ⓑ{10}^{-4}ⓒ\frac{1}{q^{-7}}ⓓ\frac{1}{2^{-4}}$

Short answer

The simplified expression of$n^{-2}=\frac{1}{n^2}$

The simplified expression of${10}^{-4}=\frac{1}{{10}^4}$

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

The simplified expression of$\frac{1}{2^{-4}}=16$

Step-by-step solution

Step 1. Given Information 

In the given question we have to simplify each expression:

$ⓐn^{-2}ⓑ{10}^{-4}ⓒ\frac{1}{q^{-7}}ⓓ\frac{1}{2^{-4}}$

Part (a) Step 1. The given expression is n−2

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

$n^{-2}=\frac{1}{n^2}$

Part (b) Step 1. The given expression is 10−4

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

${10}^{-4}=\frac{1}{{10}^4}$

Part (c) Step 1. The given expression is 1q−7

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

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

Part (d) Step 1. The given expression is 12−4

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

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