Algebra Examples

$i^{9} \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 1

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Tap for more steps...

Step 1.1

Factor out $i^{8}$ .

$i^{8} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 1.2

Rewrite $i^{8}$ as ${(i^{4})}^{2}$ .

${(i^{4})}^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 2

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 2.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

${({(i^{2})}^{2})}^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 2.2

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

${({(- 1)}^{2})}^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 2.3

Raise $- 1$ to the power of $2$ .

$1^{2} i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 3

One to any power is one.

$1 i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{25} \cdot i^{12} \cdot i^{16}$

Step 5

Rewrite $i^{25}$ as ${(i^{4})}^{6} i$ .

Tap for more steps...

Step 5.1

Factor out $i^{24}$ .

$i \cdot (i^{24} i) \cdot i^{12} \cdot i^{16}$

Step 5.2

Rewrite $i^{24}$ as ${(i^{4})}^{6}$ .

$i \cdot ({(i^{4})}^{6} i) \cdot i^{12} \cdot i^{16}$

Step 6

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 6.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$i \cdot ({({(i^{2})}^{2})}^{6} i) \cdot i^{12} \cdot i^{16}$

Step 6.2

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

$i \cdot ({({(- 1)}^{2})}^{6} i) \cdot i^{12} \cdot i^{16}$

Step 6.3

Raise $- 1$ to the power of $2$ .

$i \cdot (1^{6} i) \cdot i^{12} \cdot i^{16}$

Step 7

One to any power is one.

$i \cdot (1 i) \cdot i^{12} \cdot i^{16}$

Step 8

Multiply $i$ by $1$ .

$i \cdot i \cdot i^{12} \cdot i^{16}$

Step 9

Multiply $i i$ .

Tap for more steps...

Step 9.1

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

$i^{1} i \cdot i^{12} \cdot i^{16}$

Step 9.2

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

$i^{1} i^{1} \cdot i^{12} \cdot i^{16}$

Step 9.3

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

$i^{1 + 1} \cdot i^{12} \cdot i^{16}$

Step 9.4

Add $1$ and $1$ .

$i^{2} \cdot i^{12} \cdot i^{16}$

Step 10

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

$- 1 \cdot i^{12} \cdot i^{16}$

Step 11

Rewrite $i^{12}$ as ${(i^{4})}^{3}$ .

$- 1 \cdot {(i^{4})}^{3} \cdot i^{16}$

Step 12

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 12.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 1 \cdot {({(i^{2})}^{2})}^{3} \cdot i^{16}$

Step 12.2

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

$- 1 \cdot {({(- 1)}^{2})}^{3} \cdot i^{16}$

Step 12.3

Raise $- 1$ to the power of $2$ .

$- 1 \cdot 1^{3} \cdot i^{16}$

Step 13

One to any power is one.

$- 1 \cdot 1 \cdot i^{16}$

Step 14

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{16}$

Step 15

Rewrite $i^{16}$ as ${(i^{4})}^{4}$ .

$- 1 \cdot {(i^{4})}^{4}$

Step 16

Rewrite $i^{4}$ as $1$ .

Tap for more steps...

Step 16.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$- 1 \cdot {({(i^{2})}^{2})}^{4}$

Step 16.2

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

$- 1 \cdot {({(- 1)}^{2})}^{4}$

Step 16.3

Raise $- 1$ to the power of $2$ .

$- 1 \cdot 1^{4}$

Step 17

One to any power is one.

$- 1 \cdot 1$

Step 18

Multiply $- 1$ by $1$ .

$- 1$