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Popular >

simplify \sqrt[3]{(3x)^2}

Solution

simplify

Solution

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

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

assuming

a \geq 0

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

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{(3x)^2} ?
The solution to \sqrt[3]{(3x)^2} is 3^{2/3}x^{2/3}