Algebra Examples

$i^{20} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Step 1

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

${(i^{4})}^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Step 2

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

Tap for more steps...

Step 2.1

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

${({(i^{2})}^{2})}^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Step 2.2

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

${({(- 1)}^{2})}^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Step 2.3

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

$1^{5} \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Step 3

One to any power is one.

$1 \cdot i^{25} \cdot i^{23} \cdot i^{18}$

Step 4

Multiply $i^{25}$ by $1$ .

$i^{25} \cdot i^{23} \cdot i^{18}$

Step 5

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

Tap for more steps...

Step 5.1

Factor out $i^{24}$ .

$i^{24} i \cdot i^{23} \cdot i^{18}$

Step 5.2

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

${(i^{4})}^{6} i \cdot i^{23} \cdot i^{18}$

Step 6

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

Tap for more steps...

Step 6.1

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

${({(i^{2})}^{2})}^{6} i \cdot i^{23} \cdot i^{18}$

Step 6.2

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

${({(- 1)}^{2})}^{6} i \cdot i^{23} \cdot i^{18}$

Step 6.3

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

$1^{6} i \cdot i^{23} \cdot i^{18}$

Step 7

One to any power is one.

$1 i \cdot i^{23} \cdot i^{18}$

Step 8

Multiply $i$ by $1$ .

$i \cdot i^{23} \cdot i^{18}$

Step 9

Rewrite $i^{23}$ as ${(i^{4})}^{5} (i^{2} \cdot i)$ .

Tap for more steps...

Step 9.1

Factor out $i^{20}$ .

$i \cdot (i^{20} i^{3}) \cdot i^{18}$

Step 9.2

Rewrite $i^{20}$ as ${(i^{4})}^{5}$ .

$i \cdot ({(i^{4})}^{5} i^{3}) \cdot i^{18}$

Step 9.3

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{5} (i^{2} \cdot i)) \cdot i^{18}$

Step 10

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

Tap for more steps...

Step 10.1

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

$i \cdot ({({(i^{2})}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{18}$

Step 10.2

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

$i \cdot ({({(- 1)}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{18}$

Step 10.3

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

$i \cdot (1^{5} (i^{2} \cdot i)) \cdot i^{18}$

Step 11

One to any power is one.

$i \cdot (1 (i^{2} \cdot i)) \cdot i^{18}$

Step 12

Multiply $i^{2} \cdot i$ by $1$ .

$i \cdot (i^{2} \cdot i) \cdot i^{18}$

Step 13

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

$i \cdot (- 1 \cdot i) \cdot i^{18}$

Step 14

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

$i \cdot (- i) \cdot i^{18}$

Step 15

Multiply $i (- i)$ .

Tap for more steps...

Step 15.1

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

$- (i^{1} i) \cdot i^{18}$

Step 15.2

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

$- (i^{1} i^{1}) \cdot i^{18}$

Step 15.3

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

$- i^{1 + 1} \cdot i^{18}$

Step 15.4

Add $1$ and $1$ .

$- i^{2} \cdot i^{18}$

Step 16

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

$- - 1 \cdot i^{18}$

Step 17

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{18}$

Step 18

Multiply $i^{18}$ by $1$ .

$i^{18}$

Step 19

Rewrite $i^{18}$ as ${(i^{4})}^{4} i^{2}$ .

Tap for more steps...

Step 19.1

Factor out $i^{16}$ .

$i^{16} i^{2}$

Step 19.2

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

${(i^{4})}^{4} i^{2}$

Step 20

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

Tap for more steps...

Step 20.1

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

${({(i^{2})}^{2})}^{4} i^{2}$

Step 20.2

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

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

Step 20.3

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

$1^{4} i^{2}$

Step 21

One to any power is one.

$1 i^{2}$

Step 22

Multiply $i^{2}$ by $1$ .

$i^{2}$

Step 23

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

$- 1$