Simplify ((2x^3y^2)/(-x^2y^5))^-2

${(\frac{2 x^{3} y^{2}}{- x^{2} y^{5}})}^{- 2}$

Step 1

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

Factor $x^{2}$ out of $2 x^{3} y^{2}$ .

${(\frac{x^{2} (2 x y^{2})}{- x^{2} y^{5}})}^{- 2}$

Cancel the common factors.

Factor $x^{2}$ out of $- x^{2} y^{5}$ .

${(\frac{x^{2} (2 x y^{2})}{x^{2} (- 1 y^{5})})}^{- 2}$

Cancel the common factor.

${(\frac{x^{2} (2 x y^{2})}{x^{2} (- 1 y^{5})})}^{- 2}$

Rewrite the expression.

${(\frac{2 x y^{2}}{- 1 y^{5}})}^{- 2}$

Step 2

Cancel the common factor of $y^{2}$ and $y^{5}$ .

Factor $y^{2}$ out of $2 x y^{2}$ .

${(\frac{y^{2} (2 x)}{- 1 y^{5}})}^{- 2}$

Cancel the common factors.

Factor $y^{2}$ out of $- 1 y^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{y^{3}}{2 x}$ .

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

Apply the product rule to $\frac{y^{3}}{2 x}$ .

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

Apply the product rule to $2 x$ .

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

Step 6

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

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

Step 7

Multiply $\frac{{(y^{3})}^{2}}{2^{2} x^{2}}$ by $1$ .

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

Step 8

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

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

$\frac{y^{3 \cdot 2}}{2^{2} x^{2}}$

Multiply $3$ by $2$ .

$\frac{y^{6}}{2^{2} x^{2}}$

Step 9

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

$\frac{y^{6}}{4 x^{2}}$

Simplify ((2x^3y^2)/(-x^2y^5))^-2

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