Basic Math Examples

${(i^{3})}^{3} \cdot {(i^{2})}^{3}$

Step 1

Factor out $i^{2}$ .

${(i^{2} \cdot i)}^{3} \cdot {(i^{2})}^{3}$

Step 2

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

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

Step 3

Rewrite $- 1 i$ as $- i$ .

${(- i)}^{3} \cdot {(i^{2})}^{3}$

Step 4

Apply the product rule to $- i$ .

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

Step 5

Raise $- 1$ to the power of $3$ .

$- i^{3} \cdot {(i^{2})}^{3}$

Step 6

Factor out $i^{2}$ .

$- (i^{2} \cdot i) \cdot {(i^{2})}^{3}$

Step 7

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

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

Step 8

Rewrite $- 1 i$ as $- i$ .

$- - i \cdot {(i^{2})}^{3}$

Step 9

Multiply $- 1$ by $- 1$ .

$1 i \cdot {(i^{2})}^{3}$

Step 10

Multiply $i$ by $1$ .

$i \cdot {(i^{2})}^{3}$

Step 11

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

$i \cdot {(- 1)}^{3}$

Step 12

Raise $- 1$ to the power of $3$ .

$i \cdot - 1$

Step 13

Move $- 1$ to the left of $i$ .

$- 1 \cdot i$

Step 14

Rewrite $- 1 i$ as $- i$ .

$- i$

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