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Popular >

simplify \sqrt[5]{(32)^4}

Solution

simplify

Solution

16

Solution steps

Apply radical rule:

= ((32)^{4})^{\frac{1}{5}}

Apply exponent rule:

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

= (32)^{4 \cdot \frac{1}{5}}

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

= (32)^{\frac{4}{5}}

Factor the number:

32 = 2^{5}

= (2^{5})^{\frac{4}{5}}

Apply exponent rule:

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

(2^{5})^{\frac{4}{5}} = 2^{5 \cdot \frac{4}{5}} = 2^{4}

= 2^{4}

Refine

= 16

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{(32)^4} ?
The solution to \sqrt[5]{(32)^4} is 16