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Popular >

simplify \sqrt[10]{32^5}

Solution

simplify

Solution

42

+1

Solution steps

Apply radical rule:

= (3 2^{5})^{\frac{1}{10}}

Apply exponent rule:

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

= 3 2^{5 \cdot \frac{1}{10}}

5 \cdot \frac{1}{10} = \frac{1}{2}

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

a^{\frac{1}{2}} = a

= 32

Prime factorization of

32 : 2^{5}

= 2^{5}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 2^{4} \cdot 2

Apply radical rule:

= 2 2^{4}

Apply radical rule:

2^{4} = 2^{\frac{4}{2}} = 2^{2}

= 2^{2} 2

Refine

= 42

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Frequently Asked Questions (FAQ)

What is \sqrt[10]{32^5} ?
The solution to \sqrt[10]{32^5} is 4sqrt(2)