What is (-3x^3*y^2*z)*((-1)/(3*x*y^2))^3 ?

The solution to (-3x^3*y^2*z)*((-1)/(3*x*y^2))^3 is z/(9y^4)

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simplify (-3x^3y^2z)((-1)/(3x*y^2))^3

simplify

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

\frac{z}{9 y ^{4}}

Solution steps

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

Apply rule:

(- a) = - a

(- 3 x^{3} y^{2} z) = - 3 x^{3} y^{2} z

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

Simplify

(\frac{- 1}{3 x y ^{2}})^{3} : - \frac{1}{27 x ^{3} y ^{6}}

= - 3 x^{3} y^{2} z (- \frac{1}{27 x ^{3} y ^{6}})

Apply rule:

- a (- b) = ab

- 3 x^{3} y^{2} z (- \frac{1}{27 x ^{3} y ^{6}}) = 3 x^{3} y^{2} z \frac{1}{27 x ^{3} y ^{6}}

= 3 x^{3} y^{2} z \frac{1}{27 x ^{3} y ^{6}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 x ^{3} y ^{2} z \cdot 1}{27 x ^{3} y ^{6}}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{3 x ^{3} y ^{2} z}{27 x ^{3} y ^{6}}

Cancel the common factor:

x^{3}

= \frac{3 y ^{2} z}{27 y ^{6}}

Factor the number:

27 = 3 \cdot 9

= \frac{3 y ^{2} z}{3 \cdot 9 y ^{6}}

Cancel the common factor:

3

= \frac{y ^{2} z}{9 y ^{6}}

Simplify

\frac{y ^{2}}{y ^{6}} : \frac{1}{y ^{4}}

= \frac{z}{9 y ^{4}}

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What is (-3x^3*y^2*z)*((-1)/(3*x*y^2))^3 ?
The solution to (-3x^3*y^2*z)*((-1)/(3*x*y^2))^3 is z/(9y^4)