Use the Law of Exponents to rewrite and simplify the expression. $\frac{\sqrt{a \sqrt{b}}}{\sqrt[7]{a b}}$
A) $a^{\frac{5}{14}} b^{\frac{3}{28}}$
B) $\frac{a}{b^{\frac{3}{28}}}$
C) $\frac{a}{b}$
D) $\frac{a^{\frac{5}{14}}}{b^{\frac{3}{28}}}$
E) $\left(\frac{a}{b}\right)^{\frac{5}{14}}$

Question

Quizplus · Accepted Answer

Using the Law of Exponents:

$$\frac{\sqrt{a \sqrt{b}}}{\sqrt[7]{a b}} = a^{\frac{1}{2}} b^{\frac{1}{4}} \cdot a^{-\frac{1}{7}} b^{-\frac{1}{7}}$$

$$=a^{\frac{5}{14}}b^{\frac{3}{28}}$$

Therefore, the answer is D.

Use the Law of Exponents to Rewrite and Simplify the Expression