Evaluate i^17i^30i^6*i^19

$i^{17} \cdot i^{30} \cdot i^{6} \cdot i^{19}$

Step 1

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

Factor out $i^{16}$ .

$i^{16} i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

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

${(i^{4})}^{4} i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

Step 2

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

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

${({(i^{2})}^{2})}^{4} i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

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

${({(- 1)}^{2})}^{4} i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

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

$1^{4} i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

Step 3

One to any power is one.

$1 i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{30} \cdot i^{6} \cdot i^{19}$

Step 5

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

Factor out $i^{28}$ .

$i \cdot (i^{28} i^{2}) \cdot i^{6} \cdot i^{19}$

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

$i \cdot ({(i^{4})}^{7} i^{2}) \cdot i^{6} \cdot i^{19}$

Step 6

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

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

$i \cdot ({({(i^{2})}^{2})}^{7} i^{2}) \cdot i^{6} \cdot i^{19}$

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

$i \cdot ({({(- 1)}^{2})}^{7} i^{2}) \cdot i^{6} \cdot i^{19}$

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

$i \cdot (1^{7} i^{2}) \cdot i^{6} \cdot i^{19}$

Step 7

One to any power is one.

$i \cdot (1 i^{2}) \cdot i^{6} \cdot i^{19}$

Step 8

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

$i \cdot i^{2} \cdot i^{6} \cdot i^{19}$

Step 9

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

$i \cdot - 1 \cdot i^{6} \cdot i^{19}$

Step 10

Move $- 1$ to the left of $i$ .

$- 1 \cdot i \cdot i^{6} \cdot i^{19}$

Step 11

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

$- i \cdot i^{6} \cdot i^{19}$

Step 12

Factor out $i^{4}$ .

$- i \cdot (i^{4} i^{2}) \cdot i^{19}$

Step 13

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

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

$- i \cdot ({(i^{2})}^{2} i^{2}) \cdot i^{19}$

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

$- i \cdot ({(- 1)}^{2} i^{2}) \cdot i^{19}$

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

$- i \cdot (1 i^{2}) \cdot i^{19}$

Step 14

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

$- i \cdot i^{2} \cdot i^{19}$

Step 15

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

$- i \cdot - 1 \cdot i^{19}$

Step 16

Multiply $- 1$ by $- 1$ .

$1 i \cdot i^{19}$

Step 17

Multiply $i$ by $1$ .

$i \cdot i^{19}$

Step 18

Rewrite $i^{19}$ as ${(i^{4})}^{4} (i^{2} \cdot i)$ .

Factor out $i^{16}$ .

$i \cdot (i^{16} i^{3})$

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

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

Factor out $i^{2}$ .

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

Step 19

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

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

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

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

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

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

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

Step 20

One to any power is one.

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

Step 21

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

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

Step 22

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

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

Step 23

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

$i \cdot (- i)$

Step 24

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 25

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

$- - 1$

Step 26

Multiply $- 1$ by $- 1$ .

$1$

Evaluate i^17*i^30*i^6*i^19

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Evaluate i^17i^30i^6*i^19