Algebra Examples

(- 2 + 2 i) {(- 5 i)}^{3}

$(- 2 + 2 i) {(- 5 i)}^{3}$

Step 1

Apply the product rule to

$- 5 i$ .

$(- 2 + 2 i) ({(- 5)}^{3} i^{3})$

Step 2

Raise

$- 5$ to the power of

$3$ .

$(- 2 + 2 i) (- 125 i^{3})$

Step 3

Factor out

$i^{2}$ .

$(- 2 + 2 i) (- 125 (i^{2} \cdot i))$

Step 4

Rewrite

$i^{2}$ as

$- 1$ .

$(- 2 + 2 i) (- 125 (- 1 \cdot i))$

Step 5

Simplify the expression.

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Step 5.1

Rewrite

$- 1 i$ as

$- i$ .

$(- 2 + 2 i) (- 125 (- i))$

Step 5.2

Multiply

$- 1$ by

$- 125$ .

$(- 2 + 2 i) (125 i)$

$(- 2 + 2 i) (125 i)$

Step 6

Apply the distributive property.

$- 2 (125 i) + 2 i (125 i)$

Step 7

Multiply

$125$ by

$- 2$ .

$- 250 i + 2 i (125 i)$

Step 8

Multiply

$2 i (125 i)$ .

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Step 8.1

Multiply

$125$ by

$2$ .

$- 250 i + 250 i i$

Step 8.2

Raise

$i$ to the power of

$1$ .

$- 250 i + 250 (i^{1} i)$

Step 8.3

Raise

$i$ to the power of

$1$ .

$- 250 i + 250 (i^{1} i^{1})$

Step 8.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 250 i + 250 i^{1 + 1}$

Step 8.5

Add

$1$ and

$1$ .

$- 250 i + 250 i^{2}$

$- 250 i + 250 i^{2}$

Step 9

Simplify each term.

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Step 9.1

Rewrite

$i^{2}$ as

$- 1$ .

$- 250 i + 250 \cdot - 1$

Step 9.2

Multiply

$250$ by

$- 1$ .

$- 250 i - 250$

$- 250 i - 250$

Step 10

Reorder

$- 250 i$ and

$- 250$ .

$- 250 - 250 i$

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