Chapter A.1, Problem 18E

Solution

Use a calculator to evaluate the expression.

  $32$ .

Given:

The given expression is ${16}^{5/4}$ .

Concept Used:

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

Calculation:

The given expression is ${16}^{5/4}$ .

Square root of ${16}^{5/4}$ is:

Let $x={16}^{5/4}$

  $\begin{array}{l}x={16}^{5/4}\\ $ x={(2\cdot 2\cdot 2\cdot 2)}^{5/4}$$ x={(2^4)}^{5/4}$x=2^5\\ x=32\end{array}$

Thus the solution of given expression ${16}^{5/4}$ is $32$ .