Simplify i^30i^20i^29*i^6

$i^{30} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

Step 1

Rewrite $i^{30}$ as ${(i^{4})}^{7} i^{2}$ .

Factor out $i^{28}$ .

$i^{28} i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

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

${(i^{4})}^{7} i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

Step 2

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

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

${({(i^{2})}^{2})}^{7} i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

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

${({(- 1)}^{2})}^{7} i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

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

$1^{7} i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

Step 3

One to any power is one.

$1 i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

Step 4

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

$i^{2} \cdot i^{20} \cdot i^{29} \cdot i^{6}$

Step 5

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

$- 1 \cdot i^{20} \cdot i^{29} \cdot i^{6}$

Step 6

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

$- 1 \cdot {(i^{4})}^{5} \cdot i^{29} \cdot i^{6}$

Step 7

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

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

$- 1 \cdot {({(i^{2})}^{2})}^{5} \cdot i^{29} \cdot i^{6}$

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

$- 1 \cdot {({(- 1)}^{2})}^{5} \cdot i^{29} \cdot i^{6}$

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

$- 1 \cdot 1^{5} \cdot i^{29} \cdot i^{6}$

Step 8

One to any power is one.

$- 1 \cdot 1 \cdot i^{29} \cdot i^{6}$

Step 9

Multiply $- 1$ by $1$ .

$- 1 \cdot i^{29} \cdot i^{6}$

Step 10

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

Factor out $i^{28}$ .

$- 1 \cdot (i^{28} i) \cdot i^{6}$

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

$- 1 \cdot ({(i^{4})}^{7} i) \cdot i^{6}$

Step 11

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

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

$- 1 \cdot ({({(i^{2})}^{2})}^{7} i) \cdot i^{6}$

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

$- 1 \cdot ({({(- 1)}^{2})}^{7} i) \cdot i^{6}$

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

$- 1 \cdot (1^{7} i) \cdot i^{6}$

Step 12

One to any power is one.

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

Step 13

Multiply $i$ by $1$ .

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

Step 14

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

$- i \cdot i^{6}$

Step 15

Factor out $i^{4}$ .

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

Step 16

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

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

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

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

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

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

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

Step 17

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

$- i \cdot i^{2}$

Step 18

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

$- i \cdot - 1$

Step 19

Multiply $- 1$ by $- 1$ .

$1 i$

Step 20

Multiply $i$ by $1$ .

$i$

Simplify i^30*i^20*i^29*i^6

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Simplify i^30i^20i^29*i^6