Chapter 9, Problem 23PT

To determine

To calculate: To simplify the expression

Answer to Problem 23PT

Expression in simplified form is $4^{12}$

Explanation of Solution

Given information: Expression is ${\left(4^2\right)}^6$

Formula Used:

Exponential identities are

  $x^a{x}^b=x^{a+b}$

  $x^a{y}^a={\left(xy\right)}^a$

  ${\left(x^a\right)}^b={\left(x\right)}^{ab}$

  $\frac{x^a}{x^b}={\left(x\right)}^{a-b}$

  $x^{-a}=\frac{1}{x^a}$

Calculation:

Expression is given as

  ${\left(4^2\right)}^6$

Simplifying the expression using exponential identity ${\left(x^a\right)}^b={\left(x\right)}^{ab}$

  $\begin{array}{l}{\left(4^2\right)}^6={\left(4\right)}^{2\times 6}\\ {\left(4^2\right)}^6=4^{12}\end{array}$

Conclusion:

Hence, expression in simplified form is $4^{12}$