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 December 17th, 2015, 03:29 AM #1 Senior Member     Joined: Jan 2012 Posts: 724 Thanks: 7 Simplify the expression Simplify the expression $\frac{10^{3n/2}\times15^{n/2}\times6^{n/6}}{45^{n/3}\times20^{2n/3}}$ and hence find its value when n = 2. The challenge I am facing here is that I can't find a common factor or base for the numerator and denominator of the given problem. Could somebody help me out? Last edited by Chikis; December 17th, 2015 at 03:42 AM.
 December 17th, 2015, 03:54 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,113 Thanks: 1909 Hint: $\displaystyle \large\frac{10^{3n/2}\times15^{n/2}\times6^{n/6}}{45^{n/3} \times 20^{2n/3}} = \frac{2^{3n/2}5^{3n/2}\times3^{n/2}5^{n/2} \times 2^{n/6}3^{n/6}}{3^{2n/3}5^{n/3} \times 2^{4n/3}5^{2n/3}}$.
 December 18th, 2015, 02:43 AM #3 Senior Member     Joined: Jan 2012 Posts: 724 Thanks: 7 When I finished simplifying, I got it in the most simplified form as $2^{n/3}\times5^n$. What do you think about the answer? When n=2, the value of the expression becomes $2^{2/3}\times25$. Last edited by skipjack; December 18th, 2015 at 04:28 AM.
 December 18th, 2015, 02:54 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,113 Thanks: 1909 You can simplify the first exponent in your answer by cancelling 2. When evaluating the expression for $n$ = 2, you should not change × to +.
 December 18th, 2015, 03:18 AM #5 Senior Member     Joined: Jan 2012 Posts: 724 Thanks: 7 I have edited the post. I hope things are right now.

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