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

1 Answer

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}