Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form.
-$\frac{\sqrt{x^{5}}}{\sqrt{x^{14}}}$

A) $x^{9 / 2}$

B) $\frac{1}{x^{19 / 2}}$

C) $\frac{1}{\mathrm{x}^{18}}$

D) $\frac{1}{x^{9 / 2}}$

Question

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form.
-$\frac{\sqrt{x^{5}}}{\sqrt{x^{14}}}$

A) $x^{9 / 2}$

B) $\frac{1}{x^{19 / 2}}$

C) $\frac{1}{\mathrm{x}^{18}}$

D) $\frac{1}{x^{9 / 2}}$

Quizplus · Accepted Answer

First, convert the square roots to rational exponents: $\sqrt{x^{5}} = x^{5/2}$ and $\sqrt{x^{14}} = x^{14/2} = x^{7}$. Then, divide $x^{5/2}$ by $x^{7}$ which is $x^{5/2} / x^{7} = x^{5/2 - 14/2} = x^{-9/2}$, which simplifies to $\frac{1}{x^{9 / 2}}$.

Write with Rational Exponents and Then Apply the Properties of Exponents