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

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

Step 1

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

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

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

Cancel the common factors.

Factor $x^{2}$ out of $5 x^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

Apply the product rule to $\frac{5 x}{2}$ .

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

Apply the product rule to $5 x$ .

$\frac{5^{2} x^{2}}{2^{2}}$

Step 4

Raise $5$ to the power of $2$ .

$\frac{25 x^{2}}{2^{2}}$

Step 5

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

$\frac{25 x^{2}}{4}$