Simplify i^18i^24i^27*i^16

$i^{18} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

Step 1

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

Factor out $i^{16}$ .

$i^{16} i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

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

${(i^{4})}^{4} i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

Step 2

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

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

${({(i^{2})}^{2})}^{4} i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

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

${({(- 1)}^{2})}^{4} i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

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

$1^{4} i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

Step 4

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

$i^{2} \cdot i^{24} \cdot i^{27} \cdot i^{16}$

Step 5

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

$- 1 \cdot i^{24} \cdot i^{27} \cdot i^{16}$

Step 6

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

$- 1 \cdot {(i^{4})}^{6} \cdot i^{27} \cdot i^{16}$

Step 7

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

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

$- 1 \cdot {({(i^{2})}^{2})}^{6} \cdot i^{27} \cdot i^{16}$

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

$- 1 \cdot {({(- 1)}^{2})}^{6} \cdot i^{27} \cdot i^{16}$

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

$- 1 \cdot 1^{6} \cdot i^{27} \cdot i^{16}$

Step 8

One to any power is one.

$- 1 \cdot 1 \cdot i^{27} \cdot i^{16}$

Step 9

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{27} \cdot i^{16}$

Step 10

Rewrite $i^{27}$ as ${(i^{4})}^{6} (i^{2} \cdot i)$ .

Factor out $i^{24}$ .

$- 1 \cdot (i^{24} i^{3}) \cdot i^{16}$

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

$- 1 \cdot ({(i^{4})}^{6} i^{3}) \cdot i^{16}$

Factor out $i^{2}$ .

$- 1 \cdot ({(i^{4})}^{6} (i^{2} \cdot i)) \cdot i^{16}$

Step 11

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

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

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

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

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

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

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

Step 12

One to any power is one.

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

Step 13

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

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

Step 14

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

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

Step 15

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

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

Step 16

Multiply $- 1$ by $- 1$ .

$1 i \cdot i^{16}$

Step 17

Multiply $i$ by $1$ .

$i \cdot i^{16}$

Step 18

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

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

Step 19

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

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

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

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

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

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

$i \cdot 1^{4}$

Step 20

One to any power is one.

$i \cdot 1$

Step 21

Multiply $i$ by $1$ .

$i$

Simplify i^18*i^24*i^27*i^16

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Simplify i^18i^24i^27*i^16