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Popular >

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

Solution

simplify

2^{10 \cdot 2}

Solution

3 2^{2}

+1

Decimal Notation

134.46322 \dots

Solution steps

(2)^{102}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{102}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 102}

\frac{1}{2} \cdot 102 = 52

= 2^{52}

Apply exponent rule:

a^{b x} = (a^{b})^{x}

2^{52} = (2^{5})^{2}

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

2^{5} = 32

= 3 2^{2}

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Frequently Asked Questions (FAQ)

What is sqrt(2)^{10*sqrt(2)} ?
The solution to sqrt(2)^{10*sqrt(2)} is 32^{sqrt(2)}