What is (sqrt((\sqrt[3]{\sqrt{2)})^6})^4 ?

The solution to (sqrt((\sqrt[3]{\sqrt{2)})^6})^4 is 4

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simplify (sqrt((\sqrt[3]{\sqrt{2)})^6})^4

simplify

4

Solution steps

Rewrite

4

2 \cdot 2

Apply exponent rule:

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

Apply exponent rule:

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

Multiply the numbers:

6 \cdot 2 = 12

Apply radical rule:

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

Apply exponent rule:

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

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

\frac{1}{3} \cdot 12 = 4

= (2)^{4}

Apply radical rule:

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

= (2^{\frac{1}{2}})^{4}

Apply exponent rule:

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

= 2^{\frac{1}{2} \cdot 4}

\frac{1}{2} \cdot 4 = 2

= 2^{2}

2^{2} = 4

= 4

5 \cdot 36

(- 3)^{2} + 4^{2}

3 - 3 cos (θ) + \frac{3}{2} sec (θ)

a \cdot a \cdot a

\frac{cosh ( x )}{1 + sinh ^{2} ( x )}

What is (sqrt((\sqrt[3]{\sqrt{2)})^6})^4 ?
The solution to (sqrt((\sqrt[3]{\sqrt{2)})^6})^4 is 4