Chapter 7.CM, Problem 1CM

To determine

To Simplify:

The given expression: ${64}^{2/3}$.

Answer to Problem 1CM

Solution:

The simplified expression of ${64}^{2/3}$ is $16$.

Explanation of Solution

Formula used:

The formulas that can be used in the given expression to obtain a simplified result are given below:

${\left(a^m\right)}^n=a^{m\cdot n}$, $a^m\cdot a^n=a^{m+n}$, $\frac{a^m}{a^n}=a^{m-n}$, $a^m\cdot b^m={\left(ab\right)}^m$, $a^{m+1}=a^m\cdot a^1$, $\frac{1}{a^m}=a^{-m}$, and $a^{\text{0}}=1$

Calculation:

The given expression is ${64}^{2/3}$.

The given expression is simplified by using the formula ${\left(a^m\right)}^n=a^{m\cdot n}$.

$\begin{array}{rll}{\left(64\right)}^{2/3}& =& {\left(4^3\right)}^{2/3}\\ & =& {\left(4\right)}^{3\cdot \frac{2}{3}}\\ & =& {\left(4\right)}^2\\ & =& 16\end{array}$.

Therefore, the simplified expression of ${64}^{2/3}$ is $16$.

Final statement:

The simplified expression of ${64}^{2/3}$ is $16$.