Simplify (x^-5x^-7y^8)/(y^2)

$\frac{x^{- 5} x^{- 7} y^{8}}{y^{2}}$

Step 1

Multiply $x^{- 5}$ by $x^{- 7}$ by adding the exponents.

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

$\frac{x^{- 5 - 7} y^{8}}{y^{2}}$

Subtract $7$ from $- 5$ .

$\frac{x^{- 12} y^{8}}{y^{2}}$

Step 2

Move $x^{- 12}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{8}}{y^{2} x^{12}}$

Step 3

Cancel the common factor of $y^{8}$ and $y^{2}$ .

Factor $y^{2}$ out of $y^{8}$ .

$\frac{y^{2} y^{6}}{y^{2} x^{12}}$

Cancel the common factors.

Factor $y^{2}$ out of $y^{2} x^{12}$ .

$\frac{y^{2} y^{6}}{y^{2} (x^{12})}$

Cancel the common factor.

$\frac{y^{2} y^{6}}{y^{2} x^{12}}$

Rewrite the expression.

$\frac{y^{6}}{x^{12}}$