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Popular >

simplify \sqrt[ 1/3 ]{\sqrt[6]{16}}

Solution

simplify

Solution

4

Solution steps

Apply radical rule:

= (1 6^{\frac{1}{6}})^{\frac{1}{\frac{1}{3}}}

Apply exponent rule:

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

= 1 6^{\frac{1}{6} \cdot \frac{1}{\frac{1}{3}}}

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

= 1 6^{\frac{1}{2}}

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

= 16

Factor the number:

16 = 4^{2}

= 4^{2}

Apply radical rule:

4^{2} = 4

= 4

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Frequently Asked Questions (FAQ)

What is \sqrt[ 1/3 ]{\sqrt[6]{16}} ?
The solution to \sqrt[ 1/3 ]{\sqrt[6]{16}} is 4