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Popular >

simplify (sqrt(-5))^6

Solution

simplify

(- 5)^{6}

Solution

- 125

Solution steps

(- 5)^{6}

- 5 = 5 i

= (5 i)^{6}

Apply exponent rule:

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

(5 i)^{6} = (5)^{6} i^{6}

= (5)^{6} i^{6}

(5)^{6} = 5^{3}

= 5^{3} i^{6}

5^{3} = 125

= 125 i^{6}

Apply exponent rule:

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

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

= 125 (i^{2})^{3}

Apply imaginary number rule:

i^{2} = - 1

= 125 (- 1)^{3}

(- 1)^{3} = - 1

= 125 (- 1)

Multiply the numbers:

125 (- 1) = - 125

= - 125

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Frequently Asked Questions (FAQ)

What is (sqrt(-5))^6 ?
The solution to (sqrt(-5))^6 is -125