Simplify (36x^5y^-3z)/(-9x^8y^2z^4)

$\frac{36 x^{5} y^{- 3} z}{- 9 x^{8} y^{2} z^{4}}$

Step 1

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

$\frac{36 x^{5} z}{- 9 x^{8} y^{2} z^{4} y^{3}}$

Step 2

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

Move $y^{3}$ .

$\frac{36 x^{5} z}{- 9 x^{8} (y^{3} y^{2}) z^{4}}$

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

$\frac{36 x^{5} z}{- 9 x^{8} y^{3 + 2} z^{4}}$

Add $3$ and $2$ .

$\frac{36 x^{5} z}{- 9 x^{8} y^{5} z^{4}}$

Step 3

Cancel the common factor of $36$ and $- 9$ .

Factor $9$ out of $36 x^{5} z$ .

$\frac{9 (4 x^{5} z)}{- 9 x^{8} y^{5} z^{4}}$

Cancel the common factors.

Factor $9$ out of $- 9 x^{8} y^{5} z^{4}$ .

$\frac{9 (4 x^{5} z)}{9 (- x^{8} y^{5} z^{4})}$

Cancel the common factor.

$\frac{9 (4 x^{5} z)}{9 (- x^{8} y^{5} z^{4})}$

Rewrite the expression.

$\frac{4 x^{5} z}{- x^{8} y^{5} z^{4}}$

Step 4

Cancel the common factor of $x^{5}$ and $x^{8}$ .

Factor $x^{5}$ out of $4 x^{5} z$ .

$\frac{x^{5} (4 z)}{- x^{8} y^{5} z^{4}}$

Cancel the common factors.

Factor $x^{5}$ out of $- x^{8} y^{5} z^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

Factor $z$ out of $4 z$ .

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

Cancel the common factors.

Factor $z$ out of $- x^{3} y^{5} z^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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

Simplify (36x^5y^-3z)/(-9x^8y^2z^4)

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