I came across a question that I was unable to solve, it involves positive and negative index numbers in the same fraction and I'm not sure how to solve that, if anyone could help me please??
$$\dfrac{\left(\frac{7a^5b^3}{5a^6b^2}\right)}{\left(\frac{7b^3a^2}{5b^5a^4}\right)}$$
Also some working out would be great so I can see how to work it out properly. Thanks!
$$\dfrac{\left(\frac{7a^5b^3}{5a^6b^2}\right)}{\left(\frac{7b^3a^2}{5b^5a^4}\right)}=\frac{7a^5b^3}{5a^6b^2}\times\frac{5b^5a^4}{7b^3a^2} =\frac{a^5b^3b^5a^4}{a^6b^2b^3a^2}=\frac{a^9b^8}{a^8b^5}=ab^3.$$
The division of a fraction is equivalent to the multiplication of its reciprocal, which is obtained by swapping the numerator and denominator.