Simplify x^-1y^-4z^-1*zx^-1

$x^{- 1} y^{- 4} z^{- 1} \cdot z x^{- 1}$

Step 1

Multiply $x^{- 1}$ by $x^{- 1}$ by adding the exponents.

Move $x^{- 1}$ .

$x^{- 1} x^{- 1} y^{- 4} z^{- 1} \cdot z$

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

$x^{- 1 - 1} y^{- 4} z^{- 1} \cdot z$

Subtract $1$ from $- 1$ .

$x^{- 2} y^{- 4} z^{- 1} \cdot z$

Step 2

Multiply $z^{- 1}$ by $z$ by adding the exponents.

Move $z$ .

$x^{- 2} y^{- 4} (z \cdot z^{- 1})$

Multiply $z$ by $z^{- 1}$ .

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

$x^{- 2} y^{- 4} (z^{1} z^{- 1})$

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

$x^{- 2} y^{- 4} z^{1 - 1}$

Subtract $1$ from $1$ .

$x^{- 2} y^{- 4} z^{0}$

Step 3

Simplify $x^{- 2} y^{- 4} z^{0}$ .

$x^{- 2} y^{- 4}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{2}} y^{- 4}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{2}} \cdot \frac{1}{y^{4}}$

Step 6

Combine.

$\frac{1 \cdot 1}{x^{2} y^{4}}$

Step 7

Multiply $1$ by $1$ .

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