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Popular >

simplify (-4i)^5

Solution

simplify

(- 4 i)^{5}

Solution

- 1024 i

Solution steps

(- 4 i)^{5}

Apply exponent rule:

(- a)^{n} = - a^{n},

if

n

is odd

(- 4 i)^{5} = - (4 i)^{5}

= - (4 i)^{5}

Apply exponent rule:

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

(4 i)^{5} = 4^{5} i^{5}

= - 4^{5} i^{5}

4^{5} = 1024

= - 1024 i^{5}

Apply exponent rule:

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

i^{5} = i^{4} i

= - 1024 i^{4} i

Simplify

i^{4} : (- 1)^{2}

= - 1024 (- 1)^{2} i

Simplify

(- 1)^{2} i : i

= - 1024 i

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Frequently Asked Questions (FAQ)

What is (-4i)^5 ?
The solution to (-4i)^5 is -1024i