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Popular >

simplify (sqrt(-2))^6

Solution

simplify

(- 2)^{6}

Solution

- 8

Solution steps

(- 2)^{6}

- 2 = 2 i

= (2 i)^{6}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

(2)^{6} = 2^{3}

= 2^{3} i^{6}

2^{3} = 8

= 8 i^{6}

Apply exponent rule:

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

i^{6} = (i^{2})^{3}

= 8 (i^{2})^{3}

Apply imaginary number rule:

i^{2} = - 1

= 8 (- 1)^{3}

(- 1)^{3} = - 1

= 8 (- 1)

Multiply the numbers:

8 (- 1) = - 8

= - 8

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Frequently Asked Questions (FAQ)

What is (sqrt(-2))^6 ?
The solution to (sqrt(-2))^6 is -8