Simplify i^35i^17i^35

$i^{35} \cdot i^{17} \cdot i^{35}$

Step 1

Rewrite $i^{35}$ as ${(i^{4})}^{8} (i^{2} \cdot i)$ .

Factor out $i^{32}$ .

$i^{32} i^{3} \cdot i^{17} \cdot i^{35}$

Rewrite $i^{32}$ as ${(i^{4})}^{8}$ .

${(i^{4})}^{8} i^{3} \cdot i^{17} \cdot i^{35}$

Factor out $i^{2}$ .

${(i^{4})}^{8} (i^{2} \cdot i) \cdot i^{17} \cdot i^{35}$

Step 2

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

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

${({(i^{2})}^{2})}^{8} (i^{2} \cdot i) \cdot i^{17} \cdot i^{35}$

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

${({(- 1)}^{2})}^{8} (i^{2} \cdot i) \cdot i^{17} \cdot i^{35}$

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

$1^{8} (i^{2} \cdot i) \cdot i^{17} \cdot i^{35}$

Step 3

One to any power is one.

$1 (i^{2} \cdot i) \cdot i^{17} \cdot i^{35}$

Step 4

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

$i^{2} \cdot i \cdot i^{17} \cdot i^{35}$

Step 5

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

$- 1 \cdot i \cdot i^{17} \cdot i^{35}$

Step 6

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

$- i \cdot i^{17} \cdot i^{35}$

Step 7

Rewrite $i^{17}$ as ${(i^{4})}^{4} i$ .

Factor out $i^{16}$ .

$- i \cdot (i^{16} i) \cdot i^{35}$

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

$- i \cdot ({(i^{4})}^{4} i) \cdot i^{35}$

Step 8

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

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

$- i \cdot ({({(i^{2})}^{2})}^{4} i) \cdot i^{35}$

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

$- i \cdot ({({(- 1)}^{2})}^{4} i) \cdot i^{35}$

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

$- i \cdot (1^{4} i) \cdot i^{35}$

Step 9

One to any power is one.

$- i \cdot (1 i) \cdot i^{35}$

Step 10

Multiply $i$ by $1$ .

$- i \cdot i \cdot i^{35}$

Step 11

Multiply $- i i$ .

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

$- (i^{1} i) \cdot i^{35}$

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

$- (i^{1} i^{1}) \cdot i^{35}$

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

$- i^{1 + 1} \cdot i^{35}$

Add $1$ and $1$ .

$- i^{2} \cdot i^{35}$

Step 12

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

$- - 1 \cdot i^{35}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{35}$

Step 14

Multiply $i^{35}$ by $1$ .

$i^{35}$

Step 15

Rewrite $i^{35}$ as ${(i^{4})}^{8} (i^{2} \cdot i)$ .

Factor out $i^{32}$ .

$i^{32} i^{3}$

Rewrite $i^{32}$ as ${(i^{4})}^{8}$ .

${(i^{4})}^{8} i^{3}$

Factor out $i^{2}$ .

${(i^{4})}^{8} (i^{2} \cdot i)$

Step 16

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

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

${({(i^{2})}^{2})}^{8} (i^{2} \cdot i)$

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

${({(- 1)}^{2})}^{8} (i^{2} \cdot i)$

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

$1^{8} (i^{2} \cdot i)$

Step 17

One to any power is one.

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

Step 18

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

$i^{2} \cdot i$

Step 19

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

$- 1 \cdot i$

Step 20

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

$- i$

Simplify i^35*i^17*i^35

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Simplify i^35i^17i^35