Simplify i^-38 - MathMaster

$i^{- 38}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{i^{38}}$

Simplify the denominator.

Tap for more steps…

Rewrite $i^{38}$ as ${(i^{4})}^{9} i^{2}$ .

Tap for more steps…

Factor out $i^{36}$ .

$\frac{1}{i^{36} i^{2}}$

Rewrite $i^{36}$ as ${(i^{4})}^{9}$ .

$\frac{1}{{(i^{4})}^{9} i^{2}}$

Rewrite $i^{4}$ as $1$ .

Tap for more steps…

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$\frac{1}{{({(i^{2})}^{2})}^{9} i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{1}{{({(- 1)}^{2})}^{9} i^{2}}$

Raise $- 1$ to the power of $2$ .

$\frac{1}{1^{9} i^{2}}$

One to any power is one.

$\frac{1}{1 i^{2}}$

Multiply $i^{2}$ by $1$ .

$\frac{1}{i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{1}{- 1}$

Divide $1$ by $- 1$ .

$- 1$

Simplify i^-38

Download our
App from the store