Algebra Examples

$\frac{2}{8 i}$

Step 1

Cancel the common factor of $2$ and $8$ .

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Step 1.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{8 i}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $8 i$ .

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

Step 1.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 (4 i)}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{4 i}$

Step 2

Multiply the numerator and denominator of $\frac{1}{4 i}$ by the conjugate of $4 i$ to make the denominator real.

$\frac{1}{4 i} \cdot \frac{i}{i}$

Step 3

Multiply.

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Step 3.1

Combine.

$\frac{1 i}{4 i i}$

Step 3.2

Multiply $i$ by $1$ .

$\frac{i}{4 i i}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

Add parentheses.

$\frac{i}{4 (i i)}$

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

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

$\frac{i}{4 i^{1 + 1}}$

Step 3.3.5

Add $1$ and $1$ .

$\frac{i}{4 i^{2}}$

Step 3.3.6

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

$\frac{i}{4 \cdot - 1}$

Step 4

Multiply $4$ by $- 1$ .

$\frac{i}{- 4}$

Step 5

Move the negative in front of the fraction.

$- \frac{i}{4}$