Evaluate i^25i^23i^33

$i^{25} \cdot i^{23} \cdot i^{33}$

Step 1

Rewrite $i^{25}$ as ${(i^{4})}^{6} i$ .

Factor out $i^{24}$ .

$i^{24} i \cdot i^{23} \cdot i^{33}$

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

${(i^{4})}^{6} i \cdot i^{23} \cdot i^{33}$

Step 2

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

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

${({(i^{2})}^{2})}^{6} i \cdot i^{23} \cdot i^{33}$

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

${({(- 1)}^{2})}^{6} i \cdot i^{23} \cdot i^{33}$

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

$1^{6} i \cdot i^{23} \cdot i^{33}$

Step 3

One to any power is one.

$1 i \cdot i^{23} \cdot i^{33}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{23} \cdot i^{33}$

Step 5

Rewrite $i^{23}$ as ${(i^{4})}^{5} (i^{2} \cdot i)$ .

Factor out $i^{20}$ .

$i \cdot (i^{20} i^{3}) \cdot i^{33}$

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

$i \cdot ({(i^{4})}^{5} i^{3}) \cdot i^{33}$

Factor out $i^{2}$ .

$i \cdot ({(i^{4})}^{5} (i^{2} \cdot i)) \cdot i^{33}$

Step 6

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

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

$i \cdot ({({(i^{2})}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{33}$

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

$i \cdot ({({(- 1)}^{2})}^{5} (i^{2} \cdot i)) \cdot i^{33}$

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

$i \cdot (1^{5} (i^{2} \cdot i)) \cdot i^{33}$

Step 7

One to any power is one.

$i \cdot (1 (i^{2} \cdot i)) \cdot i^{33}$

Step 8

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

$i \cdot (i^{2} \cdot i) \cdot i^{33}$

Step 9

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

$i \cdot (- 1 \cdot i) \cdot i^{33}$

Step 10

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

$i \cdot (- i) \cdot i^{33}$

Step 11

Multiply $i (- i)$ .

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

$- (i^{1} i) \cdot i^{33}$

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

$- (i^{1} i^{1}) \cdot i^{33}$

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

$- i^{1 + 1} \cdot i^{33}$

Add $1$ and $1$ .

$- i^{2} \cdot i^{33}$

Step 12

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

$- - 1 \cdot i^{33}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \cdot i^{33}$

Step 14

Multiply $i^{33}$ by $1$ .

$i^{33}$

Step 15

Rewrite $i^{33}$ as ${(i^{4})}^{8} i$ .

Factor out $i^{32}$ .

$i^{32} i$

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

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

Step 16

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

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

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

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

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

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

$1^{8} i$

Step 17

One to any power is one.

$1 i$

Step 18

Multiply $i$ by $1$ .

$i$

Evaluate i^25*i^23*i^33

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Evaluate i^25i^23i^33