What is (3a^3*b^{-1})^2*(((a^4))/b)^{-1} ?

The solution to (3a^3*b^{-1})^2*(((a^4))/b)^{-1} is (9a^2)/b

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simplify (3a^3b^{-1})^2(((a^4))/b)^{-1}

simplify

(3 a^{3} \cdot b^{- 1})^{2} \cdot (\frac{( a ^{4} )}{b})^{- 1}

\frac{9 a ^{2}}{b}

Solution steps

(3 a^{3} b^{- 1})^{2} (\frac{a ^{4}}{b})^{- 1}

Simplify

(3 a^{3} b^{- 1})^{2} : \frac{9 a ^{6}}{b ^{2}}

= \frac{9 a ^{6}}{b ^{2}} (\frac{a ^{4}}{b})^{- 1}

Simplify

(\frac{a ^{4}}{b})^{- 1} : \frac{b}{a ^{4}}

= \frac{9 a ^{6}}{b ^{2}} \cdot \frac{b}{a ^{4}}

Apply the fraction rule:

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

= \frac{9 a ^{6} b}{b ^{2} a ^{4}}

Simplify

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

= \frac{9 a ^{2} b}{b ^{2}}

Simplify

\frac{b}{b ^{2}} : \frac{1}{b}

= \frac{9 a ^{2}}{b}

- a^{0}

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What is (3a^3*b^{-1})^2*(((a^4))/b)^{-1} ?
The solution to (3a^3*b^{-1})^2*(((a^4))/b)^{-1} is (9a^2)/b