Simplify i^9i^10i^19*i^24

$i^{9} \cdot i^{10} \cdot i^{19} \cdot i^{24}$

Step 1

Rewrite $i^{9}$ as ${(i^{4})}^{2} i$ .

Factor out $i^{8}$ .

$i^{8} i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

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

${(i^{4})}^{2} i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

Step 2

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

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

${({(i^{2})}^{2})}^{2} i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

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

${({(- 1)}^{2})}^{2} i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

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

$1^{2} i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

Step 3

One to any power is one.

$1 i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

Step 4

Multiply $i$ by $1$ .

$i \cdot i^{10} \cdot i^{19} \cdot i^{24}$

Step 5

Rewrite $i^{10}$ as ${(i^{4})}^{2} i^{2}$ .

Factor out $i^{8}$ .

$i \cdot (i^{8} i^{2}) \cdot i^{19} \cdot i^{24}$

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

$i \cdot ({(i^{4})}^{2} i^{2}) \cdot i^{19} \cdot i^{24}$

Step 6

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

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

$i \cdot ({({(i^{2})}^{2})}^{2} i^{2}) \cdot i^{19} \cdot i^{24}$

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

$i \cdot ({({(- 1)}^{2})}^{2} i^{2}) \cdot i^{19} \cdot i^{24}$

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

$i \cdot (1^{2} i^{2}) \cdot i^{19} \cdot i^{24}$

Step 7

One to any power is one.

$i \cdot (1 i^{2}) \cdot i^{19} \cdot i^{24}$

Step 8

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

$i \cdot i^{2} \cdot i^{19} \cdot i^{24}$

Step 9

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

$i \cdot - 1 \cdot i^{19} \cdot i^{24}$

Step 10

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

$- 1 \cdot i \cdot i^{19} \cdot i^{24}$

Step 11

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

$- i \cdot i^{19} \cdot i^{24}$

Step 12

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

Factor out $i^{16}$ .

$- i \cdot (i^{16} i^{3}) \cdot i^{24}$

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

$- i \cdot ({(i^{4})}^{4} i^{3}) \cdot i^{24}$

Factor out $i^{2}$ .

$- i \cdot ({(i^{4})}^{4} (i^{2} \cdot i)) \cdot i^{24}$

Step 13

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

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

$- i \cdot ({({(i^{2})}^{2})}^{4} (i^{2} \cdot i)) \cdot i^{24}$

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

$- i \cdot ({({(- 1)}^{2})}^{4} (i^{2} \cdot i)) \cdot i^{24}$

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

$- i \cdot (1^{4} (i^{2} \cdot i)) \cdot i^{24}$

Step 14

One to any power is one.

$- i \cdot (1 (i^{2} \cdot i)) \cdot i^{24}$

Step 15

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

$- i \cdot (i^{2} \cdot i) \cdot i^{24}$

Step 16

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

$- i \cdot (- 1 \cdot i) \cdot i^{24}$

Step 17

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

$- i \cdot (- i) \cdot i^{24}$

Step 18

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$1 i i \cdot i^{24}$

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

$1 (i^{1} i) \cdot i^{24}$

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

$1 (i^{1} i^{1}) \cdot i^{24}$

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

$1 i^{1 + 1} \cdot i^{24}$

Add $1$ and $1$ .

$1 i^{2} \cdot i^{24}$

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

$i^{2} \cdot i^{24}$

Step 19

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

$- 1 \cdot i^{24}$

Step 20

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

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

Step 21

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

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

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

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

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

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

$- 1 \cdot 1^{6}$

Step 22

One to any power is one.

$- 1 \cdot 1$

Step 23

Multiply $- 1$ by $1$ .

$- 1$

Simplify i^9*i^10*i^19*i^24

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Simplify i^9i^10i^19*i^24