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Popular >

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

Solution

simplify

(4 2 a^{3})^{3}

Solution

2^{\frac{3}{4}} a^{\frac{9}{4}}

Solution steps

(4 2 a^{3})^{3}

Apply radical rule:

n a = a^{\frac{1}{n}}

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

Apply exponent rule:

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

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

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

= (2 a^{3})^{\frac{3}{4}}

Apply exponent rule:

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

= 2^{\frac{3}{4}} (a^{3})^{\frac{3}{4}}

(a^{3})^{\frac{3}{4}} : a^{\frac{9}{4}}

= 2^{\frac{3}{4}} a^{\frac{9}{4}}

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Frequently Asked Questions (FAQ)

What is (\sqrt[4]{2a^3})^3 ?
The solution to (\sqrt[4]{2a^3})^3 is 2^{3/4}a^{9/4}