Chapter 1.3, Problem 5E

To determine

To find: The expression ${\left(9\right)}^{2x}$ in terms of the expression with base $3$.

Answer to Problem 5E

The expression ${\left(9\right)}^{2x}$ is written as ${\left(3\right)}^{4x}$ in terms of expression with base $3$.

Explanation of Solution

Given information:

The expression is ${\left(9\right)}^{2x}$ and the indicated base is $3$.

Calculation:

Simplify the $9$ in the expression in terms of $3$.

  $\begin{array}{c}{\left(9\right)}^{2x}={\left(3^2\right)}^{2x}\\ ={\left(3^2\right)}^{2x}\\ =3^{4x}\left[\therefore {\left(x^a\right)}^b=x^{ab}\right]\end{array}$

Therefore, the expression ${\left(9\right)}^{2x}$ is written as ${\left(3\right)}^{4x}$ in terms of expression with base $3$.