Simplify (x^2y^-1)(x^-3y)^0

$(x^{2} y^{- 1}) {(x^{- 3} y)}^{0}$

Step 1

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

$x^{2} \frac{1}{y} {(x^{- 3} y)}^{0}$

Step 2

Combine $x^{2}$ and $\frac{1}{y}$ .

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

Step 3

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

$\frac{x^{2}}{y} {(\frac{1}{x^{3}} y)}^{0}$

Step 4

Combine $\frac{1}{x^{3}}$ and $y$ .

$\frac{x^{2}}{y} {(\frac{y}{x^{3}})}^{0}$

Step 5

Apply the product rule to $\frac{y}{x^{3}}$ .

$\frac{x^{2}}{y} \cdot \frac{y^{0}}{{(x^{3})}^{0}}$

Step 6

Combine.

$\frac{x^{2} y^{0}}{y {(x^{3})}^{0}}$

Step 7

Move $y^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{2}}{y {(x^{3})}^{0} y^{0}}$

Step 8

Simplify the denominator.

Multiply $y$ by $y^{0}$ by adding the exponents.

Move $y^{0}$ .

$\frac{x^{2}}{y^{0} y {(x^{3})}^{0}}$

Multiply $y^{0}$ by $y$ .

Raise $y$ to the power of $1$ .

$\frac{x^{2}}{y^{0} y^{1} {(x^{3})}^{0}}$

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

$\frac{x^{2}}{y^{0 + 1} {(x^{3})}^{0}}$

Add $0$ and $1$ .

$\frac{x^{2}}{y^{1} {(x^{3})}^{0}}$

Simplify $y^{1} {(x^{3})}^{0}$ .

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