Chapter A.1, Problem 45E

Solution

Convert to exponential form.

  $2x^{\frac{5}{3}}{y}^{\frac{1}{3}}$ .

Given:

The given expression is $2x\sqrt[3]{x^{2}y}$ .

Concept Used:

• The exponential form is an easier way of writing repeated multiplication involving base and exponents.

Calculation:

The given expression is $2x\sqrt[3]{x^{2}y}$ .

  $\begin{array}{c}$ 2x\sqrt[3]{x^{2}y}=2x{(x^{2}y)}^{1/3}$=2x(x^{2\cdot \frac{1}{3}}{y}^{\frac{1}{3}})\\ =2x(x^{\frac{2}{3}}{y}^{\frac{1}{3}})\\ =2(x^1\cdot x^{\frac{2}{3}})y^{\frac{1}{3}}\\ =2(x^{1+\frac{2}{3}})y^{\frac{1}{3}}\\ =2(x^{\frac{3+2}{3}})y^{\frac{1}{3}}\\ =2x^{\frac{5}{3}}{y}^{\frac{1}{3}}\end{array}$

Thus the exponential form of $2x\sqrt[3]{x^{2}y}$ is $2x^{\frac{5}{3}}{y}^{\frac{1}{3}}$ .