Algebra Examples

${(2 i)}^{7} \cdot {(- 5 i^{9})}^{2}$

Step 1

Apply the product rule to $2 i$ .

$2^{7} i^{7} \cdot {(- 5 i^{9})}^{2}$

Step 2

Raise $2$ to the power of $7$ .

$128 i^{7} \cdot {(- 5 i^{9})}^{2}$

Step 3

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

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Step 3.1

Factor out $i^{4}$ .

$128 (i^{4} i^{3}) \cdot {(- 5 i^{9})}^{2}$

Step 3.2

Factor out $i^{2}$ .

$128 (i^{4} (i^{2} \cdot i)) \cdot {(- 5 i^{9})}^{2}$

Step 4

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

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Step 4.1

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

$128 ({(i^{2})}^{2} (i^{2} \cdot i)) \cdot {(- 5 i^{9})}^{2}$

Step 4.2

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

$128 ({(- 1)}^{2} (i^{2} \cdot i)) \cdot {(- 5 i^{9})}^{2}$

Step 4.3

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

$128 (1 (i^{2} \cdot i)) \cdot {(- 5 i^{9})}^{2}$

Step 5

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

$128 (i^{2} \cdot i) \cdot {(- 5 i^{9})}^{2}$

Step 6

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

$128 (- 1 \cdot i) \cdot {(- 5 i^{9})}^{2}$

Step 7

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

$128 (- i) \cdot {(- 5 i^{9})}^{2}$

Step 8

Multiply $- 1$ by $128$ .

$- 128 i \cdot {(- 5 i^{9})}^{2}$

Step 9

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

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Step 9.1

Factor out $i^{8}$ .

$- 128 i \cdot {(- 5 (i^{8} i))}^{2}$

Step 9.2

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

$- 128 i \cdot {(- 5 ({(i^{4})}^{2} i))}^{2}$

Step 10

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

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Step 10.1

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

$- 128 i \cdot {(- 5 ({({(i^{2})}^{2})}^{2} i))}^{2}$

Step 10.2

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

$- 128 i \cdot {(- 5 ({({(- 1)}^{2})}^{2} i))}^{2}$

Step 10.3

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

$- 128 i \cdot {(- 5 (1^{2} i))}^{2}$

Step 11

One to any power is one.

$- 128 i \cdot {(- 5 (1 i))}^{2}$

Step 12

Multiply $i$ by $1$ .

$- 128 i \cdot {(- 5 i)}^{2}$

Step 13

Apply the product rule to $- 5 i$ .

$- 128 i \cdot ({(- 5)}^{2} i^{2})$

Step 14

Raise $- 5$ to the power of $2$ .

$- 128 i \cdot (25 i^{2})$

Step 15

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

$- 128 i \cdot (25 \cdot - 1)$

Step 16

Multiply $25$ by $- 1$ .

$- 128 i \cdot - 25$

Step 17

Multiply $- 25$ by $- 128$ .

$3200 i$