Chapter 7.1, Problem 3GP

To determine

To Simplify: The expression ${\left[{\left(2^2\right)}^2\right]}^4$ and choose the correct option:

$\begin{array}{l}A)2^8\\ B)2^{10}\\ C)2^{16}\\ D)2^{24}\end{array}$

Answer to Problem 3GP

The required answer is $2^{16}$ i.e. option C.

Explanation of Solution

Given information:

The expression ${\left[{\left(2^2\right)}^2\right]}^4$

Calculation:

  ${\left[{\left(2^2\right)}^2\right]}^4$

  $={\left(2^{2\cdot 2}\right)}^4$

(Power of a power)

  $={\left(2^4\right)}^4$

(Simplify)

  $=\left(2^{4\cdot 4}\right)$

(Power of a power)

  $=2^{16}$

(Simplify)