Chapter A.1, Problem 46E

Solution

Convert to exponential form.

  $x^{\frac{5}{4}}{y}^{\frac{7}{4}}$ .

Given:

The given expression is $xy\sqrt[4]{x{y}^3}$ .

Concept Used:

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

Calculation:

The given expression is $xy\sqrt[4]{x{y}^3}$ .

  $\begin{array}{c}$ xy\sqrt[4]{x{y}^3}=xy{(x{y}^3)}^{1/4}$=xy(x^{\frac{1}{4}}{y}^{3\cdot \frac{1}{4}})\\ =xy(x^{\frac{1}{4}}{y}^{\frac{3}{4}})\\ =(x^1{x}^{\frac{1}{4}})(y^1{y}^{\frac{3}{4}})\\ =x^{1+\frac{1}{4}}{y}^{1+\frac{3}{4}}\\ =x^{\frac{4+1}{4}}{y}^{\frac{4+3}{4}}\\ =x^{\frac{5}{4}}{y}^{\frac{7}{4}}\end{array}$

Thus the exponential form of $xy\sqrt[4]{x{y}^3}$ is $x^{\frac{5}{4}}{y}^{\frac{7}{4}}$ .