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Popular >

simplify \sqrt[ 5/3 ]{32^2}

Solution

simplify

Solution

64

Solution steps

Apply radical rule:

= (3 2^{2})^{\frac{1}{\frac{5}{3}}}

Apply exponent rule:

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

= 3 2^{2 \cdot \frac{1}{\frac{5}{3}}}

2 \cdot \frac{1}{\frac{5}{3}} = \frac{6}{5}

= 3 2^{\frac{6}{5}}

Factor the number:

32 = 2^{5}

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

Apply exponent rule:

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

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

= 2^{6}

Refine

= 64

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Frequently Asked Questions (FAQ)

What is \sqrt[ 5/3 ]{32^2} ?
The solution to \sqrt[ 5/3 ]{32^2} is 64