Algebra Examples

$i^{3} = (i^{2}) i$

Step 1

Since $i$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$i^{2} i = i^{3}$

Step 2

Multiply $i^{2}$ by $i$ by adding the exponents.

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Step 2.1

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

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Step 2.1.1

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

$i^{2} i^{1} = i^{3}$

Step 2.1.2

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

$i^{2 + 1} = i^{3}$

Step 2.2

Add $2$ and $1$ .

$i^{3} = i^{3}$

Step 3

Move all terms containing $i$ to the left side of the equation.

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Step 3.1

Subtract $i^{3}$ from both sides of the equation.

$i^{3} - i^{3} = 0$

Step 3.2

Subtract $i^{3}$ from $i^{3}$ .

$0 = 0$

Step 4

Since $0 = 0$ , the equation will always be true.

Always true