Negative Exponents

Key Questions

  • What is the exponent of zero property?

    I suppose you mean the fact that a number to the zero exponent is always equal to one, for example:

    3^0=1

    The intuitive explanation can be found remembering that:
    1) dividing two equal numbers gives 1;
    ex. 4/4=1
    2) The fraction of two equal numbers a to the power of m and n gives:
    a^m/a^n=a^(m-n)

    Now:
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    Gió · 1 · Dec 14 2014
  • What are Negative Exponents?

    Negative exponents are an extension of the initial exponent concept.

    To understand negative exponents ,
    first review what we mean by positive (integer) exponents

    What do we mean when we write something like:
    n^p (for now, assume that p is a positive integer.

    One definition would be that
    n^p is 1 multiplied by n, p times.

    Note that using this definition
    n^0 is 1 multiplied by n, 0 times
    i.e. n^0 = 1 (for any value of n)

    Suppose you know the value of n^p for some particular values of n and p
    but you would like to know the value of n^q for a value q less than p

    For example suppose you knew that
    2^10 = 1024 but you wanted to know what 2^9 was equal to.
    Is there a faster way than multiplying 1 by 2, 9 times?
    Yes.
    If we note that 2^9 = (2^10)/2
    we can simply divide 1024 by 2 (giving 512) to obtain 2^9

    In general if we know that the value of n^p is k
    and we want to know the value of n^q when q<p
    we can simply divide k by n^(p-q)

    With this in mind what is the value of
    n^(-t) ?
    We know that n^0 = 1
    so n^(-t) must be 1 divided by n, (0 - (-t)) times

    That is n^(-t) = 1/n^t

    As a final example consider the descending powers of 3 in the following, noting that with each line down the result is decreased by dividing the current value by 3

    3^4 = 81
    3^3 = 27
    3^2 = 9
    3^1 = 3
    3^0 = 1
    3^(-1) = 1/3
    3^(-2) = 1/9
    3^(-3) = 1/27

    Alan P. · 1 · Feb 14 2015
  • How do negative exponents affect fractions?

    Raising to the -1 power is equivalent to taking the reciprocal, so we have

    (a/b)^{-1}=b/a

    I hope that this was helpful.

    Wataru · 2 · Dec 5 2014
  • How do you simplify expressions with negative exponents?

    x^(-n) = 1/(x^n)

    Maybe you were asking for something more than this (???)

    Alan P. · 1 · Feb 28 2015
  • How do you evaluate expressions with negative exponents?

    You can start by rewriting in the following way:

    b^{-x}=1/b^x

    I hope that this was helpful.

    Wataru · 1 · Nov 6 2014

Questions

Exponents and Exponential Functions