Simplify (5x^-2y^5)/(10x^4(y^-2)^4)

$\frac{5 x^{- 2} y^{5}}{10 x^{4} {(y^{- 2})}^{4}}$

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 y^{5}}{10 x^{4} {(y^{- 2})}^{4} x^{2}}$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{5 y^{5}}{10 (x^{2} x^{4}) {(y^{- 2})}^{4}}$

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

$\frac{5 y^{5}}{10 x^{2 + 4} {(y^{- 2})}^{4}}$

Add $2$ and $4$ .

$\frac{5 y^{5}}{10 x^{6} {(y^{- 2})}^{4}}$

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5 y^{5}$ .

$\frac{5 (y^{5})}{10 x^{6} {(y^{- 2})}^{4}}$

Cancel the common factors.

Factor $5$ out of $10 x^{6} {(y^{- 2})}^{4}$ .

$\frac{5 (y^{5})}{5 (2 x^{6} {(y^{- 2})}^{4})}$

Cancel the common factor.

$\frac{5 y^{5}}{5 (2 x^{6} {(y^{- 2})}^{4})}$

Rewrite the expression.

$\frac{y^{5}}{2 x^{6} {(y^{- 2})}^{4}}$

Simplify the denominator.

Multiply the exponents in ${(y^{- 2})}^{4}$ .

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

$\frac{y^{5}}{2 x^{6} y^{- 2 \cdot 4}}$

Multiply $- 2$ by $4$ .

$\frac{y^{5}}{2 x^{6} y^{- 8}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{5}}{2 x^{6} \frac{1}{y^{8}}}$

Combine exponents.

Combine $2$ and $\frac{1}{y^{8}}$ .

$\frac{y^{5}}{x^{6} \frac{2}{y^{8}}}$

Combine $x^{6}$ and $\frac{2}{y^{8}}$ .

$\frac{y^{5}}{\frac{x^{6} \cdot 2}{y^{8}}}$

Move $2$ to the left of $x^{6}$ .

$\frac{y^{5}}{\frac{2 x^{6}}{y^{8}}}$

Multiply the numerator by the reciprocal of the denominator.

$y^{5} \frac{y^{8}}{2 x^{6}}$

Multiply $y^{5} \frac{y^{8}}{2 x^{6}}$ .

Combine $y^{5}$ and $\frac{y^{8}}{2 x^{6}}$ .

$\frac{y^{5} y^{8}}{2 x^{6}}$

Multiply $y^{5}$ by $y^{8}$ by adding the exponents.

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

$\frac{y^{5 + 8}}{2 x^{6}}$

Add $5$ and $8$ .

$\frac{y^{13}}{2 x^{6}}$