What is (sqrt(\sqrt{\sqrt{\sqrt{2)}}})^{48} ?

The solution to (sqrt(\sqrt{\sqrt{\sqrt{2)}}})^{48} is 8

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simplify (sqrt(\sqrt{\sqrt{\sqrt{2)}}})^{48}

simplify

2^{48}

8

Solution steps

2^{48}

Rewrite

48

2 \cdot 24

= 2^{2 \cdot 24}

Apply exponent rule:

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

2^{2 \cdot 24} = 2^{2}^{24}

= 2^{2}^{24}

Apply exponent rule:

2^{2} = 2

= (2)^{24}

Rewrite

24

2 \cdot 12

= (2)^{2 \cdot 12}

Apply exponent rule:

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

(2)^{2 \cdot 12} = (2)^{2}^{12}

= (2)^{2}^{12}

Apply exponent rule:

(2)^{2} = 2

= (2)^{12}

Rewrite

12

2 \cdot 6

= (2)^{2 \cdot 6}

Apply exponent rule:

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

(2)^{2 \cdot 6} = ((2)^{2})^{6}

= ((2)^{2})^{6}

Apply exponent rule:

(2)^{2} = 2

= (2)^{6}

Rewrite

6

2 \cdot 3

= (2)^{2 \cdot 3}

Apply exponent rule:

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

(2)^{2 \cdot 3} = ((2)^{2})^{3}

= ((2)^{2})^{3}

Apply exponent rule:

(2)^{2} = 2

= 2^{3}

2^{3} = 8

= 8

e^{- 15} (6 - 5 e^{- 3})

0.01 \cdot 1 0^{- 3}

e^{- 2 l n (6)}

(e^{- 9})^{\frac{8}{9}}

What is (sqrt(\sqrt{\sqrt{\sqrt{2)}}})^{48} ?
The solution to (sqrt(\sqrt{\sqrt{\sqrt{2)}}})^{48} is 8