Simplify (3x^3y^-1z^-1)/(x^-4y^0z^0)

$\frac{3 x^{3} y^{- 1} z^{- 1}}{x^{- 4} y^{0} z^{0}}$

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

$\frac{3 x^{3} z^{- 1}}{x^{- 4} y^{0} z^{0} y}$

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

$\frac{3 x^{3}}{x^{- 4} y^{0} z^{0} y z}$

Simplify the denominator.

Multiply $y^{0}$ by $y$ by adding the exponents.

Move $y$ .

$\frac{3 x^{3}}{x^{- 4} (y \cdot y^{0}) z^{0} z}$

Multiply $y$ by $y^{0}$ .

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

$\frac{3 x^{3}}{x^{- 4} (y^{1} y^{0}) z^{0} z}$

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

$\frac{3 x^{3}}{x^{- 4} y^{1 + 0} z^{0} z}$

Add $1$ and $0$ .

$\frac{3 x^{3}}{x^{- 4} y^{1} z^{0} z}$

Simplify $x^{- 4} y^{1} z^{0}$ .

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

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

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

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

Move $x^{4}$ .

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

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

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

Add $4$ and $3$ .

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