Chapter 1.3, Problem 6E

To determine

To find: The expression ${\left(16\right)}^{3x}$ in terms of the expression with base $2$.

Answer to Problem 6E

The expression ${\left(16\right)}^{3x}$ is written as ${\left(2\right)}^{12x}$ in terms of expression with base $2$.

Explanation of Solution

Given information:

The expression is ${\left(16\right)}^{3x}$ and the indicated base is $2$.

Calculation:

Simplify the $16$ in the expression in terms of $2$.

  $\begin{array}{c}{\left(16\right)}^{3x}={\left(2^4\right)}^{3x}\\ ={\left(2\right)}^{3\times 4x}\left[\therefore {\left(x^a\right)}^b=x^{ab}\right]\\ =2^{12x}\end{array}$

Therefore, the expression ${\left(16\right)}^{3x}$ is written as ${\left(2\right)}^{12x}$ in terms of expression with base $2$.