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Popular >

simplify \sqrt[3]{512^2}

Solution

simplify

Solution

64

Solution steps

Apply radical rule:

= (51 2^{2})^{\frac{1}{3}}

Apply exponent rule:

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

= 51 2^{2 \cdot \frac{1}{3}}

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

= 51 2^{\frac{2}{3}}

Factor the number:

512 = 8^{3}

= (8^{3})^{\frac{2}{3}}

Apply exponent rule:

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

(8^{3})^{\frac{2}{3}} = 8^{3 \cdot \frac{2}{3}} = 8^{2}

= 8^{2}

Refine

= 64

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{512^2} ?
The solution to \sqrt[3]{512^2} is 64