Simplify i^18i^28i^9*i^29

$i^{18} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

Step 1

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

Factor out $i^{16}$ .

$i^{16} i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

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

${(i^{4})}^{4} i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

Step 2

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

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

${({(i^{2})}^{2})}^{4} i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

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

${({(- 1)}^{2})}^{4} i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

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

$1^{4} i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

Step 4

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

$i^{2} \cdot i^{28} \cdot i^{9} \cdot i^{29}$

Step 5

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

$- 1 \cdot i^{28} \cdot i^{9} \cdot i^{29}$

Step 6

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$- 1 \cdot {(i^{4})}^{7} \cdot i^{9} \cdot i^{29}$

Step 7

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

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

$- 1 \cdot {({(i^{2})}^{2})}^{7} \cdot i^{9} \cdot i^{29}$

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

$- 1 \cdot {({(- 1)}^{2})}^{7} \cdot i^{9} \cdot i^{29}$

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

$- 1 \cdot 1^{7} \cdot i^{9} \cdot i^{29}$

Step 8

One to any power is one.

$- 1 \cdot 1 \cdot i^{9} \cdot i^{29}$

Step 9

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{9} \cdot i^{29}$

Step 10

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

Factor out $i^{8}$ .

$- 1 \cdot (i^{8} i) \cdot i^{29}$

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

$- 1 \cdot ({(i^{4})}^{2} i) \cdot i^{29}$

Step 11

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

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

$- 1 \cdot ({({(i^{2})}^{2})}^{2} i) \cdot i^{29}$

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

$- 1 \cdot ({({(- 1)}^{2})}^{2} i) \cdot i^{29}$

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

$- 1 \cdot (1^{2} i) \cdot i^{29}$

Step 12

One to any power is one.

$- 1 \cdot (1 i) \cdot i^{29}$

Step 13

Multiply $i$ by $1$ .

$- 1 \cdot i \cdot i^{29}$

Step 14

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

$- i \cdot i^{29}$

Step 15

Rewrite $i^{29}$ as ${(i^{4})}^{7} i$ .

Factor out $i^{28}$ .

$- i \cdot (i^{28} i)$

Rewrite $i^{28}$ as ${(i^{4})}^{7}$ .

$- i \cdot ({(i^{4})}^{7} i)$

Step 16

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

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

$- i \cdot ({({(i^{2})}^{2})}^{7} i)$

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

$- i \cdot ({({(- 1)}^{2})}^{7} i)$

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

$- i \cdot (1^{7} i)$

Step 17

One to any power is one.

$- i \cdot (1 i)$

Step 18

Multiply $i$ by $1$ .

$- i \cdot i$

Step 19

Multiply $- i i$ .

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

$- (i^{1} i)$

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

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

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

$- i^{1 + 1}$

Add $1$ and $1$ .

$- i^{2}$

Step 20

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

$- - 1$

Step 21

Multiply $- 1$ by $- 1$ .

$1$

Simplify i^18*i^28*i^9*i^29

Related Questions

Support LCMGCF.com by disabling your adblocker.

Simplify i^18i^28i^9*i^29