Algebra Examples

$\frac{2}{3} i \cdot \frac{3}{7} i$

Step 1

Combine $\frac{2}{3}$ and $i$ .

$\frac{2 i}{3} \cdot \frac{3}{7} \cdot i$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{2 i}{3} \cdot \frac{3}{7} \cdot i$

Step 2.2

Rewrite the expression.

$2 i \cdot \frac{1}{7} \cdot i$

$2 i \cdot \frac{1}{7} \cdot i$

Step 3

Combine $\frac{1}{7}$ and $2$ .

$\frac{2}{7} i \cdot i$

Step 4

Combine $\frac{2}{7}$ and $i$ .

$\frac{2 i}{7} \cdot i$

Step 5

Multiply $\frac{2 i}{7} i$ .

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Step 5.1

Combine $\frac{2 i}{7}$ and $i$ .

$\frac{2 i i}{7}$

Step 5.2

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

$\frac{2 (i^{1} i)}{7}$

Step 5.3

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

$\frac{2 (i^{1} i^{1})}{7}$

Step 5.4

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

$\frac{2 i^{1 + 1}}{7}$

Step 5.5

Add $1$ and $1$ .

$\frac{2 i^{2}}{7}$

$\frac{2 i^{2}}{7}$

Step 6

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

$\frac{2 \cdot - 1}{7}$

Step 7

Multiply $2$ by $- 1$ .

$\frac{- 2}{7}$

Step 8

Move the negative in front of the fraction.

$- \frac{2}{7}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{7}$

Decimal Form:

$- 0.\overline{285714}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$