What is (sqrt(\sqrt[3]{2)sqrt(2)})^8 ?

The solution to (sqrt(\sqrt[3]{2)sqrt(2)})^8 is 8\sqrt[3]{2}

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simplify (sqrt(\sqrt[3]{2)sqrt(2)})^8

simplify

Solution steps

Rewrite

8

2 \cdot 4

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

= (2^{\frac{5}{6}})^{4}

Apply exponent rule:

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

= 2^{\frac{5}{6} \cdot 4}

\frac{5}{6} \cdot 4 = \frac{10}{3}

= 2^{\frac{10}{3}}

2^{3} = 8

(19)^{2}

e^{- b t} cos (wt)

8 x^{3} e^{- 2 x^{2}}

(\frac{1}{2})^{\frac{1}{2}}

a^{n} \cdot b^{n}

What is (sqrt(\sqrt[3]{2)sqrt(2)})^8 ?
The solution to (sqrt(\sqrt[3]{2)sqrt(2)})^8 is 8\sqrt[3]{2}