What is \sqrt[3]{(x^2-4x)^2} ?

The solution to \sqrt[3]{(x^2-4x)^2} is (x^2-4x)^{2/3}

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simplify \sqrt[3]{(x^2-4x)^2}

simplify

(x^{2} - 4 x)^{\frac{2}{3}}

Solution steps

Apply radical rule:

= ((x^{2} - 4 x)^{2})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

= (x^{2} - 4 x)^{2 \cdot \frac{1}{3}}

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

= (x^{2} - 4 x)^{\frac{2}{3}}

What is \sqrt[3]{(x^2-4x)^2} ?
The solution to \sqrt[3]{(x^2-4x)^2} is (x^2-4x)^{2/3}