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Popular >

simplify i^{-5}

Solution

simplify

i^{- 5}

Solution

- i

Solution steps

i^{- 5}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

i^{- 5} = \frac{1}{i ^{5}}

= \frac{1}{i ^{5}}

Simplify

i^{5} : i

= \frac{1}{i}

Multiply by the conjugate

\frac{- i}{- i}

= \frac{1 \cdot ( - i )}{i ( - i )}

Simplify

\frac{1 \cdot ( - i )}{i ( - i )} : \frac{- i}{1}

= \frac{- i}{1}

Apply the fraction rule:

\frac{a}{1} = a

= - i

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Frequently Asked Questions (FAQ)

What is i^{-5} ?
The solution to i^{-5} is -i