Simplify (-4i)^2*(2i)^3

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

Apply the product rule to $- 4 i$ .

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

Raise $- 4$ to the power of $2$ .

$16 i^{2} \cdot {(2 i)}^{3}$

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

$16 \cdot - 1 \cdot {(2 i)}^{3}$

Multiply $16$ by $- 1$ .

$- 16 \cdot {(2 i)}^{3}$

Apply the product rule to $2 i$ .

$- 16 \cdot (2^{3} i^{3})$

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

$- 16 \cdot (8 i^{3})$

Factor out $i^{2}$ .

$- 16 \cdot (8 (i^{2} \cdot i))$

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

$- 16 \cdot (8 (- 1 \cdot i))$

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

$- 16 \cdot (8 (- i))$

Multiply $- 1$ by $8$ .

$- 16 \cdot (- 8 i)$

Multiply $- 8$ by $- 16$ .

$128 i$

Related Questions