Chapter 7.1, Problem 74PFA

To determine

To calculate: The new exponent.

Answer to Problem 74PFA

The new exponent is ${13}^{80}$ .

Explanation of Solution

Given information: The given exponent is ${\left[{\left({13}^2\right)}^5\right]}^8$ .

Calculation: : The given exponent is ${\left[{\left({13}^2\right)}^5\right]}^8$ .

  ${\left[{\left({13}^2\right)}^5\right]}^8={\left({13}^2\right)}^{5\times 8}={\left({13}^2\right)}^{40}={13}^{2\times 40}={13}^{80}$

Thus, the new exponent is ${13}^{80}$ .