Question

use the quotient rule to simplify. assume that all variables represent positive real numbers.
\sqrt3{\frac{9}{x^6}}
\sqrt3{\frac{9}{x^6}} = \square
(type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Apply quotient rule for radicals

$$\sqrt[3]{\frac{9}{x^6}} = \frac{\sqrt[3]{9}}{\sqrt[3]{x^6}}$$

Step2: Simplify denominator radical

Since $\sqrt[3]{x^6} = x^{\frac{6}{3}} = x^2$
$$\frac{\sqrt[3]{9}}{x^2}$$

Answer:

$\frac{\sqrt[3]{9}}{x^2}$