Chapter 7.3, Problem 8CYU

To determine

To simplify the given expression.

Answer to Problem 8CYU

  ${\left(\frac{1}{16}\right)}^{\frac{1}{4}}=\frac{1}{2}$

Explanation of Solution

Given:

Expression: ${\left(\frac{1}{16}\right)}^{\frac{1}{4}}$

Formula used:

  $\sqrt[b]{a^c}=a^{\frac{c}{b}}$

Calculation:

Consider the given expression,

  ${\left(\frac{1}{16}\right)}^{\frac{1}{4}}$

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

Substituting the above formula in the given expression,

  $\begin{array}{l}\Rightarrow {\left(\frac{1}{2^4}\right)}^{\frac{1}{4}}\\ \Rightarrow {\left(2^{-4}\right)}^{\frac{1}{4}}\\ \Rightarrow 2^{\frac{-4}{4}}\\ \Rightarrow 2^{-1}\\ \Rightarrow \frac{1}{2}\end{array}$

Conclusion:

Therefore, the simplified form of the equation is $\frac{1}{2}$ .