Chapter EP, Problem 7.4.15EP

To determine

To calculate: The simplified form of the expression $\sqrt[4]{a^{16}{b}^8}$ .

Answer to Problem 7.4.15EP

The simplified form of the expression $\sqrt[4]{a^{16}{b}^8}$ is $a^4{b}^2$ .

Explanation of Solution

Given information:

The expression $\sqrt[4]{a^{16}{b}^8}$ .

Formula used:

If a andb are real numbers and n is a positive integer if $a^n=b$ then a is an nth root of b .

Calculation:

Consider the expression $\sqrt[4]{a^{16}{b}^8}$ .

Recall that if a andb are real numbers and n is a positive integer if $a^n=b$ then a is an nth root of b .

Rewrite the expression as,

  $\begin{array}{c}\sqrt[4]{a^{16}{b}^8}={\left(a^{16}{b}^8\right)}^{\frac{1}{4}}\\ ={\left(a^{16}\right)}^{\frac{1}{4}}{\left(b^8\right)}^{\frac{1}{4}}\\ =a^4{b}^2\end{array}$

Thus, the simplified form of the expression $\sqrt[4]{a^{16}{b}^8}$ is $a^4{b}^2$ .