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Popular >

simplify (sqrt(-6))^6

Solution

simplify

(- 6)^{6}

Solution

- 216

Solution steps

(- 6)^{6}

- 6 = 6 i

= (6 i)^{6}

Apply exponent rule:

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

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

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

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

= 6^{3} i^{6}

6^{3} = 216

= 216 i^{6}

Apply exponent rule:

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

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

= 216 (i^{2})^{3}

Apply imaginary number rule:

i^{2} = - 1

= 216 (- 1)^{3}

(- 1)^{3} = - 1

= 216 (- 1)

Multiply the numbers:

216 (- 1) = - 216

= - 216

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Frequently Asked Questions (FAQ)

What is (sqrt(-6))^6 ?
The solution to (sqrt(-6))^6 is -216