Simplify (x^12)(y^-13)(x^-5)(y^4)

$(x^{12}) (y^{- 13}) (x^{- 5}) (y^{4})$

Multiply $x^{12}$ by $x^{- 5}$ by adding the exponents.

Move $x^{- 5}$ .

$x^{- 5} x^{12} y^{- 13} y^{4}$

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

$x^{- 5 + 12} y^{- 13} y^{4}$

Add $- 5$ and $12$ .

$x^{7} y^{- 13} y^{4}$

Multiply $y^{- 13}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$x^{7} (y^{4} y^{- 13})$

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

$x^{7} y^{4 - 13}$

Subtract $13$ from $4$ .

$x^{7} y^{- 9}$

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

$x^{7} \frac{1}{y^{9}}$

Combine $x^{7}$ and $\frac{1}{y^{9}}$ .

$\frac{x^{7}}{y^{9}}$