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Popular >

simplify \sqrt[6]{64^5}

Solution

simplify

Solution

32

Solution steps

Apply radical rule:

= (6 4^{5})^{\frac{1}{6}}

Apply exponent rule:

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

= 6 4^{5 \cdot \frac{1}{6}}

5 \cdot \frac{1}{6} = \frac{5}{6}

= 6 4^{\frac{5}{6}}

Factor the number:

64 = 2^{6}

= (2^{6})^{\frac{5}{6}}

Apply exponent rule:

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

(2^{6})^{\frac{5}{6}} = 2^{6 \cdot \frac{5}{6}} = 2^{5}

= 2^{5}

Refine

= 32

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Frequently Asked Questions (FAQ)

What is \sqrt[6]{64^5} ?
The solution to \sqrt[6]{64^5} is 32