Simplify (3x^2y^-3)/(12x^6y^3)

$\frac{3 x^{2} y^{- 3}}{12 x^{6} y^{3}}$

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 x^{2}}{12 x^{6} y^{3} y^{3}}$

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

Move $y^{3}$ .

$\frac{3 x^{2}}{12 x^{6} (y^{3} y^{3})}$

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

$\frac{3 x^{2}}{12 x^{6} y^{3 + 3}}$

Add $3$ and $3$ .

$\frac{3 x^{2}}{12 x^{6} y^{6}}$

Cancel the common factor of $3$ and $12$ .

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

$\frac{3 (x^{2})}{12 x^{6} y^{6}}$

Cancel the common factors.

Factor $3$ out of $12 x^{6} y^{6}$ .

$\frac{3 (x^{2})}{3 (4 x^{6} y^{6})}$

Cancel the common factor.

$\frac{3 x^{2}}{3 (4 x^{6} y^{6})}$

Rewrite the expression.

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

Cancel the common factor of $x^{2}$ and $x^{6}$ .

Multiply by $1$ .

$\frac{x^{2} \cdot 1}{4 x^{6} y^{6}}$

Cancel the common factors.

Factor $x^{2}$ out of $4 x^{6} y^{6}$ .

$\frac{x^{2} \cdot 1}{x^{2} (4 x^{4} y^{6})}$

Cancel the common factor.

$\frac{x^{2} \cdot 1}{x^{2} (4 x^{4} y^{6})}$

Rewrite the expression.

$\frac{1}{4 x^{4} y^{6}}$