Chapter 7.3, Problem 100PFA

To determine

To find an equivalent expression.

Answer to Problem 100PFA

  ${64}^{\frac{3}{2}}=512$

Explanation of Solution

Given:

Expression: ${64}^{\frac{3}{2}}$

Formula used:

  $a^{\frac{1}{2}}=\sqrt{a}$

Calculation:

Consider the given expression

  ${64}^{\frac{3}{2}}$

Here, 64 can be written as $8^2.$

Substituting in the above formula,

  $\begin{array}{l}$ \Rightarrow {(8^2)}^{\frac{3}{2}}$\Rightarrow 8^{\frac{2\times 3}{2}}\\ \Rightarrow 8^3\\ \Rightarrow 512\end{array}$

Conclusion:

Therefore, the equivalent expression is $512.$