Simplify 8/(-12i)

$\frac{8}{- 12 i}$

Step 1

Cancel the common factor of $8$ and $- 12$ .

Factor $4$ out of $8$ .

$\frac{4 (2)}{- 12 i}$

Cancel the common factors.

Factor $4$ out of $- 12 i$ .

$\frac{4 (2)}{4 (- 3 i)}$

Cancel the common factor.

$\frac{4 \cdot 2}{4 (- 3 i)}$

Rewrite the expression.

$\frac{2}{- 3 i}$

Step 2

Multiply the numerator and denominator of $\frac{2}{- 3 i}$ by the conjugate of $- 3 i$ to make the denominator real.

$\frac{2}{- 3 i} \cdot \frac{i}{i}$

Step 3

Multiply.

Combine.

$\frac{2 i}{- 3 i i}$

Simplify the denominator.

Add parentheses.

$\frac{2 i}{- 3 (i i)}$

Raise $i$ to the power of $1$ .

$\frac{2 i}{- 3 (i^{1} i)}$

Raise $i$ to the power of $1$ .

$\frac{2 i}{- 3 (i^{1} i^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 i}{- 3 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 i}{- 3 i^{2}}$

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

$\frac{2 i}{- 3 \cdot - 1}$

Step 4

Multiply $- 3$ by $- 1$ .

$\frac{2 i}{3}$