Chapter 7.3, Problem 74PPS

To determine

To simplify the given expression.

Answer to Problem 74PPS

  ${16}^{-\frac{3}{2}}=\frac{1}{64}$

Explanation of Solution

Given:

Expression: ${16}^{-\frac{3}{2}}$

Formula used:

  ${(a^b)}^c=a^{bc}$

Calculation:

Consider the given expression,

  $\Rightarrow {16}^{-\frac{3}{2}}$

Here, 16 can be written as $4^2.$

Substituting the above formula in the given expression,

  $\begin{array}{l}$ \Rightarrow {(4^2)}^{-\frac{3}{2}}$\Rightarrow (4^{-\frac{3\times 2}{2}})\\ \Rightarrow 4^{-3}\\ \Rightarrow \frac{1}{64}\end{array}$

Conclusion:

Therefore, the simplified form of the equation is $\frac{1}{64}$ .