Chapter 4.4, Problem 3OE

To determine

To simplify the expression

  ${\left(t^6\right)}^3$

Answer to Problem 3OE

  ${\left(t^6\right)}^3=t^{18}$

Explanation of Solution

Given:

  ${\left(t^6\right)}^3$

Concept Used:

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

Calculation:

To simplify the expression

  ${\left(t^6\right)}^3$

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

  $\begin{array}{c}{\left(t^6\right)}^3=t^{6\times 3}\\ =t^{18}\end{array}$

Thus, simplified form of given expression is

  ${\left(t^6\right)}^3=t^{18}$