Simplify (x^2(xy)^-3z^-2)/(x^-2yz^-1)

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the denominator.

Multiply $z^{- 1}$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

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

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

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

Subtract $1$ from $2$ .

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

Simplify $x^{- 2} y z^{1} {(x y)}^{3}$ .

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

Step 4

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

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

Step 5

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

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

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

Add $2$ and $2$ .

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

Step 6

Simplify the denominator.

Apply the product rule to $x y$ .

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

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

Move $y^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 7

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (x^2(xy)^-3z^-2)/(x^-2yz^-1)

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