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Popular >

simplify (\sqrt[12]{8})^5

Solution

simplify

(128)^{5}

Solution

242

+1

Decimal

2.37841 \dots

Solution steps

(128)^{5}

Factor the number:

8 = 2^{3}

= (12 2^{3})^{5}

Apply radical rule:

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

= ((2^{3})^{\frac{1}{12}})^{5}

Apply exponent rule:

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

= (2^{3})^{\frac{1}{12} \cdot 5}

\frac{1}{12} \cdot 5 = \frac{5}{12}

= (2^{3})^{\frac{5}{12}}

Apply exponent rule:

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

= 2^{3 \cdot \frac{5}{12}}

3 \cdot \frac{5}{12} = \frac{5}{4}

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

2^{\frac{5}{4}} = 242

= 242

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Frequently Asked Questions (FAQ)

What is (\sqrt[12]{8})^5 ?
The solution to (\sqrt[12]{8})^5 is 2\sqrt[4]{2}