November 1st, 2016, 07:51 PM  #1 
Member Joined: Aug 2016 From: illinois Posts: 46 Thanks: 0  Exponent rules
If you have a series with (4^k/(2^k+3^k)) can you raise the whole fraction to the kth power and have (4/2+3)^k as the new series?

November 1st, 2016, 08:06 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,310 Thanks: 1222 
no $(2^k + 3^k)\neq (2+3)^k$ 
November 7th, 2016, 04:47 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
For example, taking k= 2, $\displaystyle \frac{4^2}{2^2+ 3^2}= \frac{16}{4+ 9}= \frac{16}{13}$ but $\displaystyle \left(\frac{4}{2+ 3}\right)^2= \left(\frac{4}{5}\right)^3= \frac{16}{25}$.


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