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Q. 81

Expert-verified
Found in: Page 284

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# If ${4}^{x}=7$ , what does ${4}^{-2x}$ equal?

The value of ${4}^{-2x}$ is $1}{49}$.

See the step by step solution

## Step 1. Given Information

Given :

${4}^{x}=7$

We have to find ${4}^{-2x}$

## Step 2. Write expression to be found in terms of given expression.

${4}^{-2x}={\left({4}^{x}\right)}^{-2}$

## Step 3. Put the given value in the expression and solve.

${\left({4}^{x}\right)}^{-2}={\left(7\right)}^{-2}=1}{{7}^{2}}=1}{49}$