Simplify (16x^4y^-3z^4)/(36x^-2yz^0)

$\frac{16 x^{4} y^{- 3} z^{4}}{36 x^{- 2} y z^{0}}$

Step 1

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

$\frac{16 x^{4} z^{4}}{36 x^{- 2} y z^{0} y^{3}}$

Step 2

Simplify the denominator.

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

Move $y^{3}$ .

$\frac{16 x^{4} z^{4}}{36 x^{- 2} (y^{3} y) z^{0}}$

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

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

$\frac{16 x^{4} z^{4}}{36 x^{- 2} (y^{3} y^{1}) z^{0}}$

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

$\frac{16 x^{4} z^{4}}{36 x^{- 2} y^{3 + 1} z^{0}}$

Add $3$ and $1$ .

$\frac{16 x^{4} z^{4}}{36 x^{- 2} y^{4} z^{0}}$

Simplify $36 x^{- 2} y^{4} z^{0}$ .

$\frac{16 x^{4} z^{4}}{36 x^{- 2} y^{4}}$

Step 3

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

$\frac{16 x^{4} z^{4} x^{2}}{36 y^{4}}$

Step 4

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

Move $x^{2}$ .

$\frac{16 (x^{2} x^{4}) z^{4}}{36 y^{4}}$

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

$\frac{16 x^{2 + 4} z^{4}}{36 y^{4}}$

Add $2$ and $4$ .

$\frac{16 x^{6} z^{4}}{36 y^{4}}$

Step 5

Cancel the common factor of $16$ and $36$ .

Factor $4$ out of $16 x^{6} z^{4}$ .

$\frac{4 (4 x^{6} z^{4})}{36 y^{4}}$

Cancel the common factors.

Factor $4$ out of $36 y^{4}$ .

$\frac{4 (4 x^{6} z^{4})}{4 (9 y^{4})}$

Cancel the common factor.

$\frac{4 (4 x^{6} z^{4})}{4 (9 y^{4})}$

Rewrite the expression.

$\frac{4 x^{6} z^{4}}{9 y^{4}}$