Chapter 6.6, Problem 26PPS

To determine

Evaluate the expression ${16}^{-\frac{1}{2}}$ .

Answer to Problem 26PPS

The evaluated value of expression ${16}^{-\frac{1}{2}}$ is $\frac{1}{4}$ .

Explanation of Solution

Given information: The given expression is ${16}^{-\frac{1}{2}}$ .

Calculation: The given expression ${16}^{-\frac{1}{2}}$ can be evaluated as,

  $\begin{array}{c}{16}^{-\frac{1}{2}}={\left(4\times 4\right)}^{-\frac{1}{2}}\mathrm{.....}\left(\text{Factorizing}\right)\\ ={\left(4\right)}^{\left(2\right)\left(-\frac{1}{2}\right)}\\ ={\left(4\right)}^{-1}\\ =\frac{1}{4}\end{array}$