What is (2a^2)/(3b)*(6b^2)/(4a) ?

The solution to (2a^2)/(3b)*(6b^2)/(4a) is ab

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simplify (2a^2)/(3b)*(6b^2)/(4a)

simplify

\frac{2 a ^{2}}{3 b} \cdot \frac{6 b ^{2}}{4 a}

ab

Solution steps

\frac{2 a ^{2}}{3 b} \cdot \frac{6 b ^{2}}{4 a}

Cancel

\frac{6 b ^{2}}{4 a} : \frac{3 b ^{2}}{2 a}

= \frac{2 a ^{2}}{3 b} \cdot \frac{3 b ^{2}}{2 a}

Apply the fraction rule:

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

= \frac{2 a ^{2} \cdot 3 b ^{2}}{3 b \cdot 2 a}

Cancel the common factor:

2

= \frac{a ^{2} \cdot 3 b ^{2}}{3 ba}

Cancel the common factor:

3

= \frac{a ^{2} b ^{2}}{ba}

Simplify

\frac{a ^{2}}{a} : a

= \frac{a b ^{2}}{b}

Simplify

\frac{b ^{2}}{b} : b

= ab

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