Problem 103 - College Algebra

Question

Simplify by reducing the index of the radical. $$\sqrt[3]{x^{6}}$$

Step-by-Step Solution

Answer

The simplified form of \(\sqrt[3]{x^{6}}\) is \(x^{2}\).

Step 1: Express Radical as Fractional Exponent

Write the expression \(\sqrt[3]{x^{6}}\) as \(x^{6/3}\).

Step 2: Apply Exponent Law

Apply the exponential law \(a^{m/n}=a^{(m/n)}\) in order to reduce the expression. It simplifies to \(x^{6/3}=x^{2}\).