Simplify (3x^3y^2z^-6)/(27y^4x^2z^5)

$\frac{3 x^{3} y^{2} z^{- 6}}{27 y^{4} x^{2} z^{5}}$

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

$\frac{3 x^{3} y^{2}}{27 y^{4} x^{2} z^{5} z^{6}}$

Multiply $z^{5}$ by $z^{6}$ by adding the exponents.

Move $z^{6}$ .

$\frac{3 x^{3} y^{2}}{27 y^{4} x^{2} (z^{6} z^{5})}$

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

$\frac{3 x^{3} y^{2}}{27 y^{4} x^{2} z^{6 + 5}}$

Add $6$ and $5$ .

$\frac{3 x^{3} y^{2}}{27 y^{4} x^{2} z^{11}}$

Cancel the common factor of $3$ and $27$ .

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

$\frac{3 (x^{3} y^{2})}{27 y^{4} x^{2} z^{11}}$

Cancel the common factors.

Factor $3$ out of $27 y^{4} x^{2} z^{11}$ .

$\frac{3 (x^{3} y^{2})}{3 (9 y^{4} x^{2} z^{11})}$

Cancel the common factor.

$\frac{3 (x^{3} y^{2})}{3 (9 y^{4} x^{2} z^{11})}$

Rewrite the expression.

$\frac{x^{3} y^{2}}{9 y^{4} x^{2} z^{11}}$

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

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

$\frac{x^{2} (x y^{2})}{9 y^{4} x^{2} z^{11}}$

Cancel the common factors.

Factor $x^{2}$ out of $9 y^{4} x^{2} z^{11}$ .

$\frac{x^{2} (x y^{2})}{x^{2} (9 y^{4} z^{11})}$

Cancel the common factor.

$\frac{x^{2} (x y^{2})}{x^{2} (9 y^{4} z^{11})}$

Rewrite the expression.

$\frac{x y^{2}}{9 y^{4} z^{11}}$

Cancel the common factor of $y^{2}$ and $y^{4}$ .

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

$\frac{y^{2} x}{9 y^{4} z^{11}}$

Cancel the common factors.

Factor $y^{2}$ out of $9 y^{4} z^{11}$ .

$\frac{y^{2} x}{y^{2} (9 y^{2} z^{11})}$

Cancel the common factor.

$\frac{y^{2} x}{y^{2} (9 y^{2} z^{11})}$

Rewrite the expression.

$\frac{x}{9 y^{2} z^{11}}$