Simplify (3x^-2y)*(6xy^-3)

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

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

Move $x$ .

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

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

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

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

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

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

Subtract $2$ from $1$ .

$3 x^{- 1} y \cdot (6 y^{- 3})$

Multiply $y$ by $y^{- 3}$ by adding the exponents.

Move $y^{- 3}$ .

$3 x^{- 1} (y^{- 3} y) \cdot 6$

Multiply $y^{- 3}$ by $y$ .

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

$3 x^{- 1} (y^{- 3} y^{1}) \cdot 6$

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

$3 x^{- 1} y^{- 3 + 1} \cdot 6$

Add $- 3$ and $1$ .

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

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

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

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

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

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

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

Combine.

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

Multiply $3$ by $1$ .

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

Multiply $\frac{3}{x y^{2}} \cdot 6$ .

Combine $\frac{3}{x y^{2}}$ and $6$ .

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

Multiply $3$ by $6$ .

$\frac{18}{x y^{2}}$