What is (sqrt(\sqrt[3]{\sqrt[4]{16)}})^{12} ?

The solution to (sqrt(\sqrt[3]{\sqrt[4]{16)}})^{12} is 4

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simplify (sqrt(\sqrt[3]{\sqrt[4]{16)}})^{12}

simplify

4

Solution steps

Rewrite

12

2 \cdot 6

Apply exponent rule:

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

Apply exponent rule:

Rewrite

6

3 \cdot 2

Apply exponent rule:

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

Apply exponent rule:

= 2^{2}

2^{2} = 4

= 4

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What is (sqrt(\sqrt[3]{\sqrt[4]{16)}})^{12} ?
The solution to (sqrt(\sqrt[3]{\sqrt[4]{16)}})^{12} is 4