Simplify (2x^-2y^-2z)/(x^3z^-2)

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

Step 1

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

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

Step 2

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

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

Step 3

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

$\frac{2 z}{x^{5} z^{- 2} y^{2}}$

Step 4

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

$\frac{2 z \cdot z^{2}}{x^{5} y^{2}}$

Step 5

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

Move $z^{2}$ .

$\frac{2 (z^{2} z)}{x^{5} y^{2}}$

Multiply $z^{2}$ by $z$ .

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

$\frac{2 (z^{2} z^{1})}{x^{5} y^{2}}$

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

$\frac{2 z^{2 + 1}}{x^{5} y^{2}}$

Add $2$ and $1$ .

$\frac{2 z^{3}}{x^{5} y^{2}}$