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Popular >

simplify (sqrt(-7))^4

Solution

simplify

(- 7)^{4}

Solution

49

Solution steps

(- 7)^{4}

- 7 = 7 i

= (7 i)^{4}

Apply exponent rule:

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

(7 i)^{4} = (7)^{4} i^{4}

= (7)^{4} i^{4}

(7)^{4} = 7^{2}

= 7^{2} i^{4}

7^{2} = 49

= 49 i^{4}

Apply exponent rule:

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

i^{4} = (i^{2})^{2}

= 49 (i^{2})^{2}

Apply imaginary number rule:

i^{2} = - 1

= 49 (- 1)^{2}

(- 1)^{2} = 1

= 49 \cdot 1

Multiply the numbers:

49 \cdot 1 = 49

= 49

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Frequently Asked Questions (FAQ)

What is (sqrt(-7))^4 ?
The solution to (sqrt(-7))^4 is 49