Chapter A.1, Problem 19E

Solution

Use a calculator to evaluate the expression.

  $\frac{1}{4}$ .

Given:

The given expression is ${32}^{-2/5}$ .

Concept Used:

• Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.

Calculation:

The given expression is ${32}^{-2/5}$ .

Square root of ${32}^{-2/5}$ is:

Let $x={32}^{-2/5}$

  $\begin{array}{l}x={32}^{-2/5}\\ $ x={(2\cdot 2\cdot 2\cdot 2\cdot 2)}^{-2/5}$$ x={(2^5)}^{-2/5}$x=2^{-2}\\ x=\frac{1}{4}\end{array}$

Thus the solution of given expression ${32}^{-2/5}$ is $\frac{1}{4}$ .