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 Chikis December 17th, 2015 02:29 AM

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?

 skipjack December 17th, 2015 02:54 AM

Hint: $\displaystyle \large\frac{10^{3n/2}\times15^{n/2}\times6^{n/6}}{45^{n/3} \times 20^{2n/3}} = \frac{2^{3n/2}5^{3n/2}\times3^{n/2}5^{n/2} \times 2^{n/6}3^{n/6}}{3^{2n/3}5^{n/3} \times 2^{4n/3}5^{2n/3}}$.

 Chikis December 18th, 2015 01:43 AM

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 $2^{2/3}\times25$.

 skipjack December 18th, 2015 01:54 AM

You can simplify the first exponent in your answer by cancelling 2.

When evaluating the expression for $n$ = 2, you should not change × to +.

 Chikis December 18th, 2015 02:18 AM

I have edited the post. I hope things are right now.

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