What is (sqrt(\sqrt{\sqrt{\sqrt{5)}}})^{32} ?

The solution to (sqrt(\sqrt{\sqrt{\sqrt{5)}}})^{32} is 25

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simplify (sqrt(\sqrt{\sqrt{\sqrt{5)}}})^{32}

simplify

5^{32}

25

Solution steps

5^{32}

Rewrite

32

2 \cdot 16

= 5^{2 \cdot 16}

Apply exponent rule:

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

5^{2 \cdot 16} = 5^{2}^{16}

= 5^{2}^{16}

Apply exponent rule:

5^{2} = 5

= (5)^{16}

Rewrite

16

2 \cdot 8

= (5)^{2 \cdot 8}

Apply exponent rule:

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

(5)^{2 \cdot 8} = (5)^{2}^{8}

= (5)^{2}^{8}

Apply exponent rule:

(5)^{2} = 5

= (5)^{8}

Rewrite

8

2 \cdot 4

= (5)^{2 \cdot 4}

Apply exponent rule:

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

(5)^{2 \cdot 4} = ((5)^{2})^{4}

= ((5)^{2})^{4}

Apply exponent rule:

(5)^{2} = 5

= (5)^{4}

Rewrite

4

2 \cdot 2

= (5)^{2 \cdot 2}

Apply exponent rule:

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

(5)^{2 \cdot 2} = ((5)^{2})^{2}

= ((5)^{2})^{2}

Apply exponent rule:

(5)^{2} = 5

= 5^{2}

5^{2} = 25

= 25

e^{- 3 t} \cdot e^{- s t}

(e^{6})^{2}

1.3 e^{- 2}

1.3 e^{- 1}

e^{t x} \cdot e^{- x}

What is (sqrt(\sqrt{\sqrt{\sqrt{5)}}})^{32} ?
The solution to (sqrt(\sqrt{\sqrt{\sqrt{5)}}})^{32} is 25