What is \sqrt[3]{x^2}*\sqrt[3]{x^2} ?

The solution to \sqrt[3]{x^2}*\sqrt[3]{x^2} is cube root of x^4

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simplify \sqrt[3]{x^2}*\sqrt[3]{x^2}

simplify

Solution steps

Apply radical rule:

= (x^{2})^{\frac{1}{3}} (x^{2})^{\frac{1}{3}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(x^{2})^{\frac{1}{3}} (x^{2})^{\frac{1}{3}} = (x^{2})^{\frac{1}{3} + \frac{1}{3}}

= (x^{2})^{\frac{1}{3} + \frac{1}{3}}

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

= (x^{2})^{\frac{2}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= x^{2 \cdot \frac{2}{3}}

2 \cdot \frac{2}{3} = \frac{4}{3}

= x^{\frac{4}{3}}

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What is \sqrt[3]{x^2}*\sqrt[3]{x^2} ?
The solution to \sqrt[3]{x^2}*\sqrt[3]{x^2} is cube root of x^4