Simplify ((2x^-3y^0)/(z^4))((3x^-2z^7)/(y^-2))

$(\frac{2 x^{- 3} y^{0}}{z^{4}}) (\frac{3 x^{- 2} z^{7}}{y^{- 2}})$

Combine.

$\frac{2 x^{- 3} y^{0} (3 x^{- 2} z^{7})}{z^{4} y^{- 2}}$

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

Move $x^{- 2}$ .

$\frac{2 (x^{- 2} x^{- 3}) y^{0} (3 z^{7})}{z^{4} y^{- 2}}$

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

$\frac{2 x^{- 2 - 3} y^{0} (3 z^{7})}{z^{4} y^{- 2}}$

Subtract $3$ from $- 2$ .

$\frac{2 x^{- 5} y^{0} (3 z^{7})}{z^{4} y^{- 2}}$

Simplify.

Simplify $2 x^{- 5} y^{0} (3 z^{7})$ .

$\frac{2 x^{- 5} (3 z^{7})}{z^{4} y^{- 2}}$

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

$\frac{2 (3 z^{7})}{z^{4} y^{- 2} x^{5}}$

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

$\frac{2 (3 z^{7}) y^{2}}{z^{4} x^{5}}$

Cancel the common factor of $z^{7}$ and $z^{4}$ .

Factor $z^{4}$ out of $2 (3 z^{7}) y^{2}$ .

$\frac{z^{4} (2 (3 z^{3}) y^{2})}{z^{4} x^{5}}$

Cancel the common factors.

Factor $z^{4}$ out of $z^{4} x^{5}$ .

$\frac{z^{4} (2 (3 z^{3}) y^{2})}{z^{4} (x^{5})}$

Cancel the common factor.

$\frac{z^{4} (2 (3 z^{3}) y^{2})}{z^{4} x^{5}}$

Rewrite the expression.

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

Multiply $2$ by $3$ .

$\frac{6 z^{3} y^{2}}{x^{5}}$