Chapter 4.4, Problem 4OE

To determine

To simplify the expression

  ${\left(c^4\right)}^4$

Answer to Problem 4OE

  ${\left(c^4\right)}^4=c^{16}$

Explanation of Solution

Given:

  ${\left(c^4\right)}^4$

Concept Used:

For all integers m and n: ${\left(a^m\right)}^n=a^{mn}$

Calculation:

To simplify the expression

  ${\left(c^4\right)}^4$

Use the basic properties of power.

Simplify this using the property ${\left(a^m\right)}^n=a^{mn}$ , and then proceed further to simplify, as

  $\begin{array}{c}{\left(c^4\right)}^4=c^{4\times 4}\\ =c^{16}\end{array}$

Thus, simplified form of given expression is

  ${\left(c^4\right)}^4=c^{16}$