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Popular >

simplify (5i)^3

Solution

simplify

(5 i)^{3}

Solution

- 125 i

Solution steps

(5 i)^{3}

Apply exponent rule:

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

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

= 5^{3} i^{3}

5^{3} = 125

= 125 i^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

i^{3} = i^{2} i

= 125 i^{2} i

Apply imaginary number rule:

i^{2} = - 1

= 125 (- 1 i)

Apply rule:

1 \cdot a = a

- 1 i = - i

= 125 (- i)

Apply rule:

a (- b) = - ab

125 (- i) = - 125 i

= - 125 i

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Frequently Asked Questions (FAQ)

What is (5i)^3 ?
The solution to (5i)^3 is -125i