Evaluate ((-2x)^3(-x)^2)/((2x)^2)

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

Step 1

Cancel the common factor of ${(- 2 x)}^{3}$ and ${(2 x)}^{2}$ .

Factor $- 1$ out of $- 2 x$ .

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

Rewrite $- (2 x)$ as $- 1 (2 x)$ .

$\frac{{(- 1 (2 x))}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Apply the product rule to $- 1 (2 x)$ .

$\frac{{(- 1)}^{3} {(2 x)}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Raise $- 1$ to the power of $3$ .

$\frac{- 1 {(2 x)}^{3} {(- x)}^{2}}{{(2 x)}^{2}}$

Factor ${(2 x)}^{2}$ out of $- 1 {(2 x)}^{3} {(- x)}^{2}$ .

$\frac{{(2 x)}^{2} (- 1 (2 x) {(- x)}^{2})}{{(2 x)}^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{{(2 x)}^{2} (- 1 (2 x) {(- x)}^{2})}{{(2 x)}^{2} \cdot 1}$

Cancel the common factor.

$\frac{{(2 x)}^{2} (- 1 (2 x) {(- x)}^{2})}{{(2 x)}^{2} \cdot 1}$

Rewrite the expression.

$\frac{- 1 (2 x) {(- x)}^{2}}{1}$

Divide $- 1 (2 x) {(- x)}^{2}$ by $1$ .

$- 1 (2 x) {(- x)}^{2}$

Step 2

Simplify the expression.

Multiply $2$ by $- 1$ .

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

Apply the product rule to $- x$ .

$- 2 x ({(- 1)}^{2} x^{2})$

Rewrite using the commutative property of multiplication.

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

Step 3

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

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

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

$- 2 \cdot {(- 1)}^{2} x^{2 + 1}$

Add $2$ and $1$ .

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

Step 4

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

$- 2 \cdot 1 x^{3}$

Step 5

Multiply $- 2$ by $1$ .

$- 2 x^{3}$

Evaluate ((-2x)^3(-x)^2)/((2x)^2)

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