Chapter SH, Problem 6.19EP

To determine

Find the simplified form of the given expression.

Answer to Problem 6.19EP

The simplified form of the expression is $5^{\frac{1}{2}}\cdot x^{\frac{3}{2}}$ .

Explanation of Solution

Given:

The given expression is $\sqrt[6]{125x^9}$ .

Calculation:

Apply radical property $\sqrt[n]{x^p}=x^{\frac{p}{n}}$ .

  $\begin{array}{l}\sqrt[6]{125x^9}\\ =\sqrt[6]{125}\cdot \sqrt[6]{x^9}\\ =\sqrt[6]{5^3}\cdot \sqrt[6]{x^9}\\ =5^{\frac{3}{6}}\cdot x^{\frac{9}{6}}\\ =5^{\frac{1}{2}}\cdot x^{\frac{3}{2}}\end{array}$

Hence the simplified form of the expression is $5^{\frac{1}{2}}\cdot x^{\frac{3}{2}}$ .