Question 43251: I asked this question a few days ago, but haven't received a response. Because I am bombing when it comes to rational exponents and the radical sign; It just totally confuses me, so I'm here begging for some assistance. Can anyone please, please, help? I would be forever grateful.
"While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign, Include in your answer and example of an equation easier to solve as a rational exponent rather than a radical sign."
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Okay, here is what I would say...
Using rational exponents is a clearer, cleaner and more condensed way to express all roots in general. Using radical signs is rather clumsy, especially when you wish to combine different roots. Thus rational exponents has a clear advantage in this regard.
An example equation might be
x^(2/3) * x^(1/5) + 1 = 3
Here you can merely add the exponents together, whereas if you expressed these as roots within radical signs, you would be forced to change everything to fifteenth roots first, etc., thereby introducing a greater chance of misunderstanding and subsequent error.
To finish the problem, we get
x^(13/15) = 2
x = 2^(15/13)
How does that work for you?
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