Find the Product (-2x^2)^3*3x

${(- 2 x^{2})}^{3} \cdot 3 x$

Step 1

Rewrite using the commutative property of multiplication.

$3 {(- 2 x^{2})}^{3} x$

Step 2

Apply the product rule to $- 2 x^{2}$ .

$3 ({(- 2)}^{3} {(x^{2})}^{3}) x$

Step 3

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

$3 (- 8 {(x^{2})}^{3}) x$

Step 4

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 (- 8 x^{2 \cdot 3}) x$

Multiply $2$ by $3$ .

$3 (- 8 x^{6}) x$

Step 5

Multiply $x^{6}$ by $x$ by adding the exponents.

Move $x$ .

$3 (- 8 (x \cdot x^{6}))$

Multiply $x$ by $x^{6}$ .

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

$3 (- 8 (x^{1} x^{6}))$

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

$3 (- 8 x^{1 + 6})$

Add $1$ and $6$ .

$3 (- 8 x^{7})$

Step 6

Multiply $- 8$ by $3$ .

$- 24 x^{7}$