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

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

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

simplify

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

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

assuming

a \geq 0

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

3 \cdot \frac{1}{4} = \frac{3}{4}

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

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