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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!

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    $\begingroup$ It would help make your post more readable if you were to type it using MathJax. Please check that how it now appears matches what is intended. $\endgroup$ – JMoravitz Aug 14 '16 at 2:58
  • $\begingroup$ Yes that is correct @JMoravitz $\endgroup$ – Kiwi Aug 14 '16 at 3:02
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$$\dfrac{\left(\frac{7a^5b^3}{5a^6b^2}\right)}{\left(\frac{7b^3a^2}{5b^5a^4}\right)}=\frac{7a^5b^3}{5a^6b^2}\times\frac{5b^5a^4}{7b^3a^2} =\frac{a^5b^3b^5a^4}{a^6b^2b^3a^2}=\frac{a^9b^8}{a^8b^5}=ab^3.$$

The division of a fraction is equivalent to the multiplication of its reciprocal, which is obtained by swapping the numerator and denominator.

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