Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fractional Exponents (How is it done?)

  1. Aug 2, 2014 #1
    How does 2^5/2 become 2^2 multiplied by 2^1/2?
    (The '^' means 'to the power of' so 2 to the power of 5/2. I am not sure how to write this as an exponent as this is my first post.)

    2^5/2 = 2^2 × 2^1/2

    So 2^2 = 4 and 2^1/2 means Square Root so there is a radical sign, so it becomes √2.

    I tried to reverse engineer the solution but I'm still not sure how 2^5/2 makes it. I know you first Square root it so √2 then you put to the power of 5 so √2^5. This goes into decimals so I am confused on what to do next. I looked at the solution and I can see that both of them make 2^5/2 I just don't know how it was factorized into those specific numbers, because 4 x √2 = 4√2 and somehow that is √2^5? I know 2^5 also makes 32.

    So I think I might of done something wrong or I don't know the correct method, can someone please attempt to help me and thank you for your time!
  2. jcsd
  3. Aug 2, 2014 #2
    Do you agree that x^(a+b)=(x^a) (x^b) for natural x,a,b?

    edit, forgot a +
    Last edited: Aug 2, 2014
  4. Aug 2, 2014 #3
    In my case would that be 2^5/2 (5 is a and 2 is b) = (2^5) (5^2)? I'm quite sure I'm doing something wrong so I think I can't agree on that even though I think its correct.

    So what is a and b? If a and b are 5 and 2 they make (2^5) (5^2) making 800. I am kind of lost... Am I getting it wrong?

    Another go at it I see that 2^5 = 32 and 5^2 = 25 - So do I put in the fraction making it 2^5/1 and 5^1/2?

    Oh now I see it and the '+', Thank you for changing it
    Last edited: Aug 2, 2014
  5. Aug 2, 2014 #4
    Do you agree that
    [itex]2^4 = 2^2 * 2^2[/itex]
    [itex]3^{10}=3^4 * 3^6[/itex]
    Last edited: Aug 2, 2014
  6. Aug 2, 2014 #5
    Yes, Because when you are multiplying powers you add them together, but since I started fractional exponents I am very confused - probably because of the fractions.

    So if you added 2^2 and 2^1/2 that would make 2^3/2 if i am correct or 2.5?

    Okay so there's 2/1 + 1/2 = 2 5/2
    So adding fractions you double it to make it 4/2 then add it to make it 5/2 making it 2^5/2.
    So we done this backwards but how did 2^5/2 split up to make those 2?

    Oh wait (Edit), So you could also spilt it up to something else? But it has to be a Fractional Exponents because so it can be combined? Not sure why it has to be a fractional exponent but I know you split the expression into the product of an integer exponent and the factor with a fractional coefficient less than one. I think the reason why this is done is so you can keep the root in the equation, otherwise it no longer has a fractional exponent.

    Thank you for your valuable time, which you were very helpful!

    PS. If I made any mistakes please correct (:
    Last edited: Aug 2, 2014
  7. Aug 2, 2014 #6
  8. Aug 2, 2014 #7


    User Avatar
    2015 Award

    Staff: Mentor

    2^5/2 is problematic, it could mean ##\frac{2^5}{2}##. You can write it as 2^(5/2) or better [noparse]25/2[/noparse], which gets parsed as 25/2. And you can use LaTeX here.

    You can split up the 5/2 like this:
    And then use the rule for exponents written above.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Fractional Exponents (How is it done?)
  1. Fractional exponents (Replies: 4)