Simplify (x^4y^-2z^3)/(x^-5y^2z)

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

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

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

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

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

$\frac{x^{4} z^{3}}{x^{- 5} y^{2 + 2} z}$

Add $2$ and $2$ .

$\frac{x^{4} z^{3}}{x^{- 5} y^{4} z}$

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

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

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

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

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

$\frac{x^{5 + 4} z^{3}}{y^{4} z}$

Add $5$ and $4$ .

$\frac{x^{9} z^{3}}{y^{4} z}$

Cancel the common factor of $z^{3}$ and $z$ .

Factor $z$ out of $x^{9} z^{3}$ .

$\frac{z (x^{9} z^{2})}{y^{4} z}$

Cancel the common factors.

Factor $z$ out of $y^{4} z$ .

$\frac{z (x^{9} z^{2})}{z y^{4}}$

Cancel the common factor.

$\frac{z (x^{9} z^{2})}{z y^{4}}$

Rewrite the expression.

$\frac{x^{9} z^{2}}{y^{4}}$