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

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

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

simplify

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

b^{4}

Solution steps

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

Simplify

\frac{a ^{3}}{b ^{- 2}} : a^{3} b^{2}

= a^{3} b^{2} \frac{a b ^{2}}{a ^{4}}

Cancel

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

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

Cross-cancel common factor:

a^{3}

= b^{2} b^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

b^{2} b^{2} = b^{2 + 2}

= b^{2 + 2}

Add the numbers:

2 + 2 = 4

= b^{4}

\frac{2}{3} \times \frac{1}{4}

\frac{14}{10}

\frac{x ^{2} - 9}{x ^{2} + 5 x + 6} - \frac{3 x - 14}{4 x + 8}

\frac{1}{3} \cdot (- 2)

(2 x - 3) (3 x^{2} - x - 5)

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