Simplify (625(5xy)^-3)/((5x)^2y^7)

$\frac{625 {(5 x y)}^{- 3}}{{(5 x)}^{2} y^{7}}$

Move ${(5 x y)}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{625}{{(5 x)}^{2} y^{7} {(5 x y)}^{3}}$

Simplify the denominator.

Apply the product rule to $5 x$ .

$\frac{625}{5^{2} x^{2} y^{7} {(5 x y)}^{3}}$

Apply the product rule to $5 x y$ .

$\frac{625}{5^{2} x^{2} y^{7} {(5 x)}^{3} y^{3}}$

Multiply $y^{7}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$\frac{625}{5^{2} x^{2} (y^{3} y^{7}) {(5 x)}^{3}}$

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

$\frac{625}{5^{2} x^{2} y^{3 + 7} {(5 x)}^{3}}$

Add $3$ and $7$ .

$\frac{625}{5^{2} x^{2} y^{10} {(5 x)}^{3}}$

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

$\frac{625}{25 x^{2} y^{10} {(5 x)}^{3}}$

Apply the product rule to $5 x$ .

$\frac{625}{25 x^{2} y^{10} (5^{3} x^{3})}$

Raise $5$ to the power of $3$ .

$\frac{625}{25 x^{2} y^{10} \cdot 125 x^{3}}$

Combine exponents.

Multiply $125$ by $25$ .

$\frac{625}{3125 x^{2} y^{10} x^{3}}$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{625}{3125 (x^{3} x^{2}) y^{10}}$

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

$\frac{625}{3125 x^{3 + 2} y^{10}}$

Add $3$ and $2$ .

$\frac{625}{3125 x^{5} y^{10}}$

Cancel the common factor of $625$ and $3125$ .

Factor $625$ out of $625$ .

$\frac{625 (1)}{3125 x^{5} y^{10}}$

Cancel the common factors.

Factor $625$ out of $3125 x^{5} y^{10}$ .

$\frac{625 (1)}{625 (5 x^{5} y^{10})}$

Cancel the common factor.

$\frac{625 \cdot 1}{625 (5 x^{5} y^{10})}$

Rewrite the expression.

$\frac{1}{5 x^{5} y^{10}}$