Simplify i^13i^11i^29*i^15

$i^{13} \cdot i^{11} \cdot i^{29} \cdot i^{15}$

Step 1

Rewrite $i^{13}$ as ${(i^{4})}^{3} i$ .

Factor out $i^{12}$ .

$i^{12} i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

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

${(i^{4})}^{3} i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

Step 2

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

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

${({(i^{2})}^{2})}^{3} i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

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

${({(- 1)}^{2})}^{3} i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

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

$1^{3} i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

Step 3

One to any power is one.

$1 i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{11} \cdot i^{29} \cdot i^{15}$

Step 5

Rewrite $i^{11}$ as ${(i^{4})}^{2} (i^{2} \cdot i)$ .

Factor out $i^{8}$ .

$i \cdot (i^{8} i^{3}) \cdot i^{29} \cdot i^{15}$

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

$i \cdot ({(i^{4})}^{2} i^{3}) \cdot i^{29} \cdot i^{15}$

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{2} (i^{2} \cdot i)) \cdot i^{29} \cdot i^{15}$

Step 6

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

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

$i \cdot ({({(i^{2})}^{2})}^{2} (i^{2} \cdot i)) \cdot i^{29} \cdot i^{15}$

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

$i \cdot ({({(- 1)}^{2})}^{2} (i^{2} \cdot i)) \cdot i^{29} \cdot i^{15}$

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

$i \cdot (1^{2} (i^{2} \cdot i)) \cdot i^{29} \cdot i^{15}$

Step 7

One to any power is one.

$i \cdot (1 (i^{2} \cdot i)) \cdot i^{29} \cdot i^{15}$

Step 8

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

$i \cdot (i^{2} \cdot i) \cdot i^{29} \cdot i^{15}$

Step 9

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

$i \cdot (- 1 \cdot i) \cdot i^{29} \cdot i^{15}$

Step 10

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

$i \cdot (- i) \cdot i^{29} \cdot i^{15}$

Step 11

Multiply $i (- i)$ .

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

$- (i^{1} i) \cdot i^{29} \cdot i^{15}$

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

$- (i^{1} i^{1}) \cdot i^{29} \cdot i^{15}$

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

$- i^{1 + 1} \cdot i^{29} \cdot i^{15}$

Add $1$ and $1$ .

$- i^{2} \cdot i^{29} \cdot i^{15}$

Step 12

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

$- - 1 \cdot i^{29} \cdot i^{15}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{29} \cdot i^{15}$

Step 14

Multiply $i^{29}$ by $1$ .

$i^{29} \cdot i^{15}$

Step 15

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

Factor out $i^{28}$ .

$i^{28} i \cdot i^{15}$

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

${(i^{4})}^{7} i \cdot i^{15}$

Step 16

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

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

${({(i^{2})}^{2})}^{7} i \cdot i^{15}$

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

${({(- 1)}^{2})}^{7} i \cdot i^{15}$

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

$1^{7} i \cdot i^{15}$

Step 17

One to any power is one.

$1 i \cdot i^{15}$

Step 18

Multiply $i$ by $1$ .

$i \cdot i^{15}$

Step 19

Rewrite $i^{15}$ as ${(i^{4})}^{3} (i^{2} \cdot i)$ .

Factor out $i^{12}$ .

$i \cdot (i^{12} i^{3})$

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

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

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{3} (i^{2} \cdot i))$

Step 20

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

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

$i \cdot ({({(i^{2})}^{2})}^{3} (i^{2} \cdot i))$

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

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

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

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

Step 21

One to any power is one.

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

Step 22

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

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

Step 23

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

$i \cdot (- 1 \cdot i)$

Step 24

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

$i \cdot (- i)$

Step 25

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 26

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

$- - 1$

Step 27

Multiply $- 1$ by $- 1$ .

$1$

Simplify i^13*i^11*i^29*i^15

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Simplify i^13i^11i^29*i^15