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Popular >

simplify (sqrt(2))^{11}

Solution

simplify

(2)^{11}

Solution

322

+1

Decimal Notation

45.25483 \dots

Solution steps

(2)^{11}

Apply exponent rule:

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

(2)^{10 + 1} = (2)^{10} 2

= (2)^{10} 2

(2)^{10} = ((2)^{2})^{5}

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

Apply exponent rule:

(2)^{2} = 2

= 2^{5} 2

2^{5} = 32

= 322

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Frequently Asked Questions (FAQ)

What is (sqrt(2))^{11} ?
The solution to (sqrt(2))^{11} is 32sqrt(2)