Simplify (5x^2y)/(2x^-1y^3)

$\frac{5 x^{2} y}{2 x^{- 1} y^{3}}$

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

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

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

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

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

$\frac{5 (x^{1} x^{2}) y}{2 y^{3}}$

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

$\frac{5 x^{1 + 2} y}{2 y^{3}}$

Add $1$ and $2$ .

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

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

Factor $y$ out of $5 x^{3} y$ .

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

Cancel the common factors.

Factor $y$ out of $2 y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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