Chapter 4.2, Problem 9QR

To determine

To Express: The given radicals into rational powers.

Answer to Problem 9QR

The required expression is $x^{\frac{3}{2}}-x^{\frac{5}{6}}$ .

Explanation of Solution

Given information: $\sqrt{x}(x-\sqrt[3]{x})$ .

Formula used: $\sqrt[n]{x}=x^{\frac{1}{n}},x^a\times x^b=x^{a+b}$ .

Calculation:

  $\begin{array}{l}\sqrt{x}(x-\sqrt[3]{x})\\ =x^{\frac{1}{2}}(x-x^{\frac{1}{3}})\\ =x^{\frac{1}{2}}\times x-x^{\frac{1}{2}}\times x^{\frac{1}{3}}\\ =x^{\frac{1}{2}+1}-x^{\frac{1}{2}+\frac{1}{3}}\\ =x^{\frac{3}{2}}-x^{\frac{5}{6}}\end{array}$