What is ((3x)/y)^2((2y)/(3x))^3 ?

The solution to ((3x)/y)^2((2y)/(3x))^3 is (8y)/(3x)

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simplify ((3x)/y)^2((2y)/(3x))^3

simplify

(\frac{3 x}{y})^{2} (\frac{2 y}{3 x})^{3}

\frac{8 y}{3 x}

Solution steps

(\frac{3 x}{y})^{2} (\frac{2 y}{3 x})^{3}

Simplify

(\frac{3 x}{y})^{2} : \frac{9 x ^{2}}{y ^{2}}

= \frac{9 x ^{2}}{y ^{2}} (\frac{2 y}{3 x})^{3}

Simplify

(\frac{2 y}{3 x})^{3} : \frac{8 y ^{3}}{27 x ^{3}}

= \frac{9 x ^{2}}{y ^{2}} \cdot \frac{8 y ^{3}}{27 x ^{3}}

Apply the fraction rule:

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

= \frac{9 x ^{2} \cdot 8 y ^{3}}{y ^{2} \cdot 27 x ^{3}}

Factor the number:

27 = 9 \cdot 3

= \frac{9 x ^{2} \cdot 8 y ^{3}}{y ^{2} \cdot 9 \cdot 3 x ^{3}}

Cancel the common factor:

9

= \frac{x ^{2} \cdot 8 y ^{3}}{y ^{2} \cdot 3 x ^{3}}

Simplify

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

= \frac{x ^{2} \cdot 8 y}{3 x ^{3}}

Simplify

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

= \frac{8 y}{3 x}

3 x^{2} - 8 x = 1

(1 6^{\frac{3}{2}})^{\frac{1}{2}}

3 - 9

3 y^{2} + 40 y - 28

5 (6 - 2 y) + 4 y = 6

What is ((3x)/y)^2((2y)/(3x))^3 ?
The solution to ((3x)/y)^2((2y)/(3x))^3 is (8y)/(3x)