Question 120370

{{{((-3a^2b)/(35a^5))*((14a^3b^2)/(-9b^4))}}} Start with the given expression



{{{((-3a^2b)*(14a^3b^2))/((35a^5)*(-9b^4))}}} Combine the fractions



{{{(-42a^5b^3)/(-315a^5b^4)}}} Multiply the numerators and denominators by adding the exponents. Remember {{{x^2*x^3=x^(2+3)=x^5}}}. Don't forget to multiply the coefficients.



{{{(2/15)a^0b^-1}}} Divide the expression by subtracting the exponents. Remember {{{x^5/x^3=x^(5-3)=x^2}}}. Don't forget to divide the coefficients.




{{{(2/15)(1/b)}}} Rewrite {{{a^0}}} as 1 and remove it (since multiplication by 1 doesn't affect the result). Rewrite {{{b^-1}}} as {{{1/b}}}



{{{2/15b}}} Combine the fractions




So {{{((-3a^2b)/(35a^5))*((14a^3b^2)/(-9b^4))}}} simplifies to {{{2/15b}}} 


In other words, {{{((-3a^2b)/(35a^5))*((14a^3b^2)/(-9b^4))=2/15b}}}