What is (\frac{81xz^3)/(36y)}{(27x^2z^2)/(12xy)} ?

The solution to (\frac{81xz^3)/(36y)}{(27x^2z^2)/(12xy)} is z

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simplify (\frac{81xz^3)/(36y)}{(27x^2z^2)/(12xy)}

simplify

\frac{\frac{81 x z ^{3}}{36 y}}{\frac{27 x ^{2} z ^{2}}{12 x y}}

z

Solution steps

\frac{\frac{81 x z ^{3}}{36 y}}{\frac{27 x ^{2} z ^{2}}{12 x y}}

Apply the fraction rule:

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

= \frac{81 x z ^{3} \cdot 12 x y}{36 y \cdot 27 x ^{2} z ^{2}}

Cancel the common factor:

y

= \frac{81 x z ^{3} \cdot 12 x}{36 \cdot 27 x ^{2} z ^{2}}

Apply exponent rule:

aa = a^{2}

xx = x^{2}

= \frac{81 x ^{2} z ^{3} \cdot 12}{36 \cdot 27 x ^{2} z ^{2}}

Cancel the common factor:

x^{2}

= \frac{81 z ^{3} \cdot 12}{36 \cdot 27 z ^{2}}

Factor the number:

81 = 27 \cdot 3

= \frac{27 \cdot 3 z ^{3} \cdot 12}{36 \cdot 27 z ^{2}}

Cancel the common factor:

27

= \frac{3 z ^{3} \cdot 12}{36 z ^{2}}

Factor the number:

36 = 3 \cdot 12

= \frac{3 z ^{3} \cdot 12}{3 \cdot 12 z ^{2}}

Cancel the common factor:

3

= \frac{z ^{3} \cdot 12}{12 z ^{2}}

Cancel the common factor:

12

= \frac{z ^{3}}{z ^{2}}

Simplify

\frac{z ^{3}}{z ^{2}} : z

= z

\frac{5}{3 2}

- 8 1^{\frac{3}{4}}

\frac{22}{15}

(- 2 - 10 i) + (3 - 4 i)

\frac{\frac{x ^{2} - 64}{x - 8}}{\frac{x ^{2} + 5 x - 24}{3 x}}

What is (\frac{81xz^3)/(36y)}{(27x^2z^2)/(12xy)} ?
The solution to (\frac{81xz^3)/(36y)}{(27x^2z^2)/(12xy)} is z