Question

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

Short answer

The value of$4^{-2x}$is$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$49$}\right.$.

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.

$4^{-2x}={(4^x)}^{-2}$

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

${\left(4^x\right)}^{-2}={\left(7\right)}^{-2}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$7^2$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$49$}\right.$