Fractional Exponents

Key Questions

  • How do you convert radical expressions to fractional exponents?

    The reciprocal of the number associated with the radical is the power needed.

    Examples:

    root3(5)=5^(1/3)
    root7(2)=2^(1/7)

    If the radicand (number under the radical sign) has a power in it, the same method still works:

    root4(9^2)=9^(2/4)

    This can be simplified to get 9^(1/2).

    Rishi A. · 1 · Dec 14 2014
  • How do you evaluate fractional exponents?

    x^(a/b) =rootb(x^a) = (rootb(x))^a

    You can just remember this rule, or you can learn about why this is:

    fractional exponent 1/b

    So first we're going to look at an expression of the form: x^(1/b).
    To investigate what this means, we need to go from x to x^(1/b) and then deduce something from it.

    x^1 = x^(b/b) = x^(1/b*b)
    What does multiplication mean? Repeated addition. So we can instead of multiplying by b, adding the number to itself b times.
    x^(1/b+1/b+1/b+1/b +...) (b times)

    There is a rule you use when multiplying numbers with the same radical: add the exponents. If we reverse this rule, we get:
    x^(1/b)*x^(1/b)*x^(1/b)*x^(1/b)*x^(1/b)... (b times)

    Now, we still know that this number is equal to x. So now we have to think a bit. What number, multiplied by itself b times, gives you x.
    It's the bth-root of x => x^(1/b)=rootbx

    For example: 8^(1/3)
    If we multiply this by itself 3 times we get:
    8^(1/3)*8^(1/3)*8^(1/3) = 8^(3/3) = 8
    What number multiplied by itself 3 times, gives you 8.
    It's of course root3(8) = 2

    What about a/b?
    To know what x^(a/b) means, we can further rely on our previous findings:
    x^(a/b) = x^(a*1/b) = x^(1/b+1/b+1/b+1/b...) (a times)
    = x^(1/b)*x^(1/b)*x^(1/b)... (a times)

    Repeated multiplication is equal to exponentiation, so we can write:
    = (x^(1/b))^a = (rootbx)^a

    You can also bring the exponent in the root:
    = rootb(x^a)

    Nico Ekkart · 1 · Dec 20 2014
  • How do you simplify fractional exponents?

    We can rewrite:

    b^{m/n}=root{n}{b^m}

    Example

    3^{5/7}=root{7}{3^5}

    I hope that this was helpful.

    Wataru · 1 · Nov 12 2014
  • What are Fractional Exponents?

    I will show you what fractional exponents are

    Suppose we are asked to simplify this :

    (16)^(1/4)

    Basically this means that we have to find the 4^(th) root of 16

    so in the form of a picture it will be like thisenter image source here

    Sidharth · 1 · Jan 12 2015

Questions

Exponents and Exponential Functions