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Popular >

simplify (sqrt(\sqrt{2)})^{10}

Solution

simplify

(2)^{10}

Solution

42

+1

Decimal Notation

5.65685 \dots

Solution steps

(2)^{10}

Rewrite

10

as

2 \cdot 5

= (2)^{2 \cdot 5}

Apply exponent rule:

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

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

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

Apply exponent rule:

(2)^{2} = 2

= (2)^{5}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(2)^{4 + 1} = (2)^{4} 2

= (2)^{4} 2

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

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

Apply exponent rule:

(2)^{2} = 2

= 2^{2} 2

2^{2} = 4

= 42

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Frequently Asked Questions (FAQ)

What is (sqrt(\sqrt{2)})^{10} ?
The solution to (sqrt(\sqrt{2)})^{10} is 4sqrt(2)