Simplify (2i)^3*(5i)

${(2 i)}^{3} \cdot (5 i)$

Step 1

Apply the product rule to $2 i$ .

$2^{3} i^{3} \cdot (5 i)$

Step 2

Raise $2$ to the power of $3$ .

$8 i^{3} \cdot (5 i)$

Step 3

Factor out $i^{2}$ .

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

Step 4

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

$8 (- 1 \cdot i) \cdot (5 i)$

Step 5

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

$8 (- i) \cdot (5 i)$

Step 6

Multiply $- 1$ by $8$ .

$- 8 i \cdot (5 i)$

Step 7

Multiply $- 8 i (5 i)$ .

Multiply $5$ by $- 8$ .

$- 40 i i$

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

$- 40 (i^{1} i)$

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

$- 40 (i^{1} i^{1})$

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

$- 40 i^{1 + 1}$

Add $1$ and $1$ .

$- 40 i^{2}$

Step 8

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

$- 40 \cdot - 1$

Step 9

Multiply $- 40$ by $- 1$ .

$40$