Evaluate (12x^6y^-4z^2)/(3x^2y^-6z^3)

$\frac{12 x^{6} y^{- 4} z^{2}}{3 x^{2} y^{- 6} z^{3}}$

Step 1

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{12 x^{6} y^{- 4} z^{2} y^{6}}{3 x^{2} z^{3}}$

Step 2

Multiply $y^{- 4}$ by $y^{6}$ by adding the exponents.

Move $y^{6}$ .

$\frac{12 x^{6} (y^{6} y^{- 4}) z^{2}}{3 x^{2} z^{3}}$

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

$\frac{12 x^{6} y^{6 - 4} z^{2}}{3 x^{2} z^{3}}$

Subtract $4$ from $6$ .

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

Step 3

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

Factor $3$ out of $12 x^{6} y^{2} z^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{4 x^{4} y^{2} z^{2}}{z^{3}}$

Step 5

Cancel the common factor of $z^{2}$ and $z^{3}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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