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Popular >

simplify 5i^{-5}

Solution

simplify

5 i^{- 5}

Solution

- 5 i

Solution steps

5 i^{- 5}

Apply exponent rule:

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

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

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

Simplify

i^{5} : i

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

Multiply by the conjugate

\frac{- i}{- i}

= 5 \cdot \frac{1 \cdot ( - i )}{i ( - i )}

Simplify

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

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

Apply the fraction rule:

\frac{a}{1} = a

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

= 5 (- i)

Apply rule:

a (- b) = - ab

5 (- i) = - 5 i

= - 5 i

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Frequently Asked Questions (FAQ)

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