Question

How do you simplify `\frac { a ^ { 2} b ^ { - 5} } { 3a ^ { 5} } \cdot \frac { b } { a ^ { - 4} }`?

Answer 1

`a/{3b^4}`

Explanation:

Given that

`\frac{a^2b^{-5}}{3a^5}\cdot \frac{b}{a^{-4}}`

`=1/3\cdot a^2b^{-5} a^{-5}\cdot a^4b\quad (\because \ x^{-1}=1/x\ \forall \ \ x\ne 0)`

`=1/3(a^2\cdot a^{-5}\cdot a^4)(b^{-5}\cdot b)`

`=1/3(a^{2-5+4})(b^{-5+1})`

`=1/3(a^{1})(b^{-4})`

`=1/3(a)(1/b^{4})`

`=a/{3b^4}`