Question

\frac{\sqrt{x^4}}{\sqrt3{x}}

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Convert radicals to rational exponents

$$ \sqrt{x^4} = x^{\frac{4}{2}} = x^2 $$

$$ \sqrt[3]{x} = x^{\frac{1}{3}} $$

Step 2: Apply the quotient rule of exponents

$$ \frac{x^2}{x^{\frac{1}{3}}} = x^{2 - \frac{1}{3}} $$

$$ 2 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3} $$

$$ x^{\frac{5}{3}} $$

Step 3: Convert back to radical form

$$ x^{\frac{5}{3}} = \sqrt[3]{x^5} = x\sqrt[3]{x^2} $$

Answer:

$$ x^{\frac{5}{3}} \text{ or } x\sqrt[3]{x^2} $$