Q. 5.30 - Intermediate Algebra

Question

Simplify each expression:

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

Step-by-Step Solution

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 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 1 q − 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 1 2 − 4

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

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