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    Using Exponents in Algebra

    You might like to read the page on Exponents first.

    Whole Number Exponents

    The exponent "n" in an says
    how many times to use a in a multiplication:


    Example: 53 = 5 × 5 × 5 = 125

    • The "3" says to use 5 three times in a multiplication
    • In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

    Negative Exponents

    A negative exponent a-n is equal to 1/an (1 divided by the positive exponent)

    Example:

    5-3 = 1/53 = 1/125 = 0.008

    Also ...

    by changing the signs of the exponents we get:

    A positive exponent an is equal to 1/a-n (1 divided by the negative exponent)

    So, we can move an expression between the top and bottom (numerator and denominator) of a fraction when we also change the sign of the exponent.

    Example: 5-3 = 1/53 = 1/125 = 0.008

    Positive and Negative Together

    Here is an example with positive and negative exponents:

    Example: 432-59-132

    We can put the values with negative exponents at the bottom (remembering to make the exponents positive):

    433

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