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

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

Step 1

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

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

Step 2

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

Move $y^{3}$ .

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

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

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

$\frac{2 x^{2} z^{4}}{6 x^{2} (y^{3} y^{1}) z^{3}}$

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

$\frac{2 x^{2} z^{4}}{6 x^{2} y^{3 + 1} z^{3}}$

Add $3$ and $1$ .

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

Step 3

Cancel the common factor of $2$ and $6$ .

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

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

Cancel the common factors.

Factor $2$ out of $6 x^{2} y^{4} z^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $z^{4}$ and $z^{3}$ .

Factor $z^{3}$ out of $z^{4}$ .

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

Cancel the common factors.

Factor $z^{3}$ out of $3 y^{4} z^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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