Simplify (36x^-4y^2z^0)/(5x^2y^-3z^-2)

$\frac{36 x^{- 4} y^{2} z^{0}}{5 x^{2} y^{- 3} z^{- 2}}$

Step 1

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

$\frac{36 y^{2}}{5 x^{2} y^{- 3} z^{- 2} x^{4}}$

Step 2

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{36 y^{2}}{5 (x^{4} x^{2}) y^{- 3} z^{- 2}}$

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

$\frac{36 y^{2}}{5 x^{4 + 2} y^{- 3} z^{- 2}}$

Add $4$ and $2$ .

$\frac{36 y^{2}}{5 x^{6} y^{- 3} z^{- 2}}$

Step 3

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

$\frac{36 y^{2} y^{3}}{5 x^{6} z^{- 2}}$

Step 4

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

$\frac{36 y^{2} y^{3} z^{2}}{5 x^{6}}$

Step 5

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

Move $y^{3}$ .

$\frac{36 (y^{3} y^{2}) z^{2}}{5 x^{6}}$

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

$\frac{36 y^{3 + 2} z^{2}}{5 x^{6}}$

Add $3$ and $2$ .

$\frac{36 y^{5} z^{2}}{5 x^{6}}$