Simplify (27x^-2y^6)/(3x^5y^2z^0)

$\frac{27 x^{- 2} y^{6}}{3 x^{5} y^{2} z^{0}}$

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{27 y^{6}}{3 x^{5} y^{2} z^{0} x^{2}}$

Simplify the denominator.

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{27 y^{6}}{3 (x^{2} x^{5}) y^{2} z^{0}}$

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

$\frac{27 y^{6}}{3 x^{2 + 5} y^{2} z^{0}}$

Add $2$ and $5$ .

$\frac{27 y^{6}}{3 x^{7} y^{2} z^{0}}$

Simplify $3 x^{7} y^{2} z^{0}$ .

$\frac{27 y^{6}}{3 x^{7} y^{2}}$

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

Factor $3$ out of $27 y^{6}$ .

$\frac{3 (9 y^{6})}{3 x^{7} y^{2}}$

Cancel the common factors.

Factor $3$ out of $3 x^{7} y^{2}$ .

$\frac{3 (9 y^{6})}{3 (x^{7} y^{2})}$

Cancel the common factor.

$\frac{3 (9 y^{6})}{3 (x^{7} y^{2})}$

Rewrite the expression.

$\frac{9 y^{6}}{x^{7} y^{2}}$

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

Factor $y^{2}$ out of $9 y^{6}$ .

$\frac{y^{2} (9 y^{4})}{x^{7} y^{2}}$

Cancel the common factors.

Factor $y^{2}$ out of $x^{7} y^{2}$ .

$\frac{y^{2} (9 y^{4})}{y^{2} x^{7}}$

Cancel the common factor.

$\frac{y^{2} (9 y^{4})}{y^{2} x^{7}}$

Rewrite the expression.

$\frac{9 y^{4}}{x^{7}}$