Question

\sqrt3{x^7} =

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Convert radical to rational exponent

$$ \sqrt[n]{a^m} = a^{\frac{m}{n}} $$

$$ \sqrt[3]{x^7} = x^{\frac{7}{3}} $$

Step 2: Simplify the fraction

$$ \frac{7}{3} = 2 + \frac{1}{3} $$

$$ x^{\frac{7}{3}} = x^{2 + \frac{1}{3}} = x^2 \cdot x^{\frac{1}{3}} = x^2\sqrt[3]{x} $$

Answer:

$$ x^{\frac{7}{3}} \quad \text{or} \quad x^2\sqrt[3]{x} $$