Simplify (5x^2y^-5)/(10x^6y^10)

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

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

$\frac{5 x^{2}}{10 x^{6} y^{10} y^{5}}$

Multiply $y^{10}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

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

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

$\frac{5 x^{2}}{10 x^{6} y^{5 + 10}}$

Add $5$ and $10$ .

$\frac{5 x^{2}}{10 x^{6} y^{15}}$

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

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

$\frac{5 (x^{2})}{10 x^{6} y^{15}}$

Cancel the common factors.

Factor $5$ out of $10 x^{6} y^{15}$ .

$\frac{5 (x^{2})}{5 (2 x^{6} y^{15})}$

Cancel the common factor.

$\frac{5 x^{2}}{5 (2 x^{6} y^{15})}$

Rewrite the expression.

$\frac{x^{2}}{2 x^{6} y^{15}}$

Cancel the common factor of $x^{2}$ and $x^{6}$ .

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{2 x^{6} y^{15}}$

Cancel the common factors.

Factor $x^{2}$ out of $2 x^{6} y^{15}$ .

$\frac{x^{2} \cdot 1}{x^{2} (2 x^{4} y^{15})}$

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (2 x^{4} y^{15})}$

Rewrite the expression.

$\frac{1}{2 x^{4} y^{15}}$