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

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

Step 1

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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

Step 3

Simplify the denominator.

Multiply $y^{- 3}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

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

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

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

Subtract $3$ from $4$ .

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

Simplify $3 x^{2} y^{1} z^{4}$ .

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

Multiply $z^{4}$ by $z^{3}$ by adding the exponents.

Move $z^{3}$ .

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

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

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

Add $3$ and $4$ .

$\frac{2 x^{4}}{3 x^{2} y z^{7}}$

Step 4

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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