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Popular >

simplify (sqrt(-7))^6

Solution

simplify

(- 7)^{6}

Solution

- 343

Solution steps

(- 7)^{6}

- 7 = 7 i

= (7 i)^{6}

Apply exponent rule:

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

(7 i)^{6} = (7)^{6} i^{6}

= (7)^{6} i^{6}

(7)^{6} = 7^{3}

= 7^{3} i^{6}

7^{3} = 343

= 343 i^{6}

Apply exponent rule:

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

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

= 343 (i^{2})^{3}

Apply imaginary number rule:

i^{2} = - 1

= 343 (- 1)^{3}

(- 1)^{3} = - 1

= 343 (- 1)

Multiply the numbers:

343 (- 1) = - 343

= - 343

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Frequently Asked Questions (FAQ)

What is (sqrt(-7))^6 ?
The solution to (sqrt(-7))^6 is -343