Simplify (6x)/(5y)*(y^2x^-2)/(x^3)

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

Combine.

$\frac{6 x (y^{2} x^{- 2})}{5 y x^{3}}$

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

Move $x^{- 2}$ .

$\frac{6 (x^{- 2} x) y^{2}}{5 y x^{3}}$

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

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

$\frac{6 (x^{- 2} x^{1}) y^{2}}{5 y x^{3}}$

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

$\frac{6 x^{- 2 + 1} y^{2}}{5 y x^{3}}$

Add $- 2$ and $1$ .

$\frac{6 x^{- 1} y^{2}}{5 y x^{3}}$

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

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

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

Move $x$ .

$\frac{6 y^{2}}{5 y (x \cdot x^{3})}$

Multiply $x$ by $x^{3}$ .

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

$\frac{6 y^{2}}{5 y (x^{1} x^{3})}$

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

$\frac{6 y^{2}}{5 y x^{1 + 3}}$

Add $1$ and $3$ .

$\frac{6 y^{2}}{5 y x^{4}}$

Cancel the common factor of $y^{2}$ and $y$ .

Factor $y$ out of $6 y^{2}$ .

$\frac{y (6 y)}{5 y x^{4}}$

Cancel the common factors.

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

$\frac{y (6 y)}{y (5 x^{4})}$

Cancel the common factor.

$\frac{y (6 y)}{y (5 x^{4})}$

Rewrite the expression.

$\frac{6 y}{5 x^{4}}$