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November 1st, 2016, 06:51 PM   #1
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Question 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?
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November 1st, 2016, 07:06 PM   #2
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no

$(2^k + 3^k)\neq (2+3)^k$
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November 7th, 2016, 03:47 PM   #3
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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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