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Popular >

simplify (sqrt(\sqrt{\sqrt{2)}})^8

Solution

simplify

(2)^{8}

Solution

2

Solution steps

(2)^{8}

Rewrite

8

as

2 \cdot 4

= (2)^{2 \cdot 4}

Apply exponent rule:

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

(2)^{2 \cdot 4} = (2)^{2}^{4}

= (2)^{2}^{4}

Apply exponent rule:

(2)^{2} = 2

= (2)^{4}

Rewrite

4

as

2 \cdot 2

= (2)^{2 \cdot 2}

Apply exponent rule:

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

(2)^{2 \cdot 2} = ((2)^{2})^{2}

= ((2)^{2})^{2}

Apply exponent rule:

(2)^{2} = 2

= (2)^{2}

Apply exponent rule:

(2)^{2} = 2

= 2

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Frequently Asked Questions (FAQ)

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