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Popular >

simplify \sqrt[3]{\sqrt[7]{8}}

Solution

simplify

Solution

+1

Decimal Notation

1.10408 \dots

Solution steps

Apply radical rule:

= (8^{\frac{1}{7}})^{\frac{1}{3}}

Apply exponent rule:

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

= 8^{\frac{1}{7} \cdot \frac{1}{3}}

\frac{1}{7} \cdot \frac{1}{3} = \frac{1}{21}

= 8^{\frac{1}{21}}

Factor the number:

8 = 2^{3}

Apply exponent rule:

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

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{\sqrt[7]{8}} ?
The solution to \sqrt[3]{\sqrt[7]{8}} is \sqrt[7]{2}