Simplify (x^-2y^3)/(x^3z^-1)

$\frac{x^{- 2} y^{3}}{x^{3} z^{- 1}}$

Step 1

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

$\frac{y^{3}}{x^{3} z^{- 1} x^{2}}$

Step 2

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

Move $x^{2}$ .

$\frac{y^{3}}{x^{2} x^{3} z^{- 1}}$

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

$\frac{y^{3}}{x^{2 + 3} z^{- 1}}$

Add $2$ and $3$ .

$\frac{y^{3}}{x^{5} z^{- 1}}$

Step 3

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

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