> Rules of Exponent

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Rules of Exponents

  • In the algebraic expression, where  is raised to the power ,  is called a base and  is called an exponent. Here are the basic rules of exponents, where the bases  and  are nonzero real numbers and the exponents  and  are integers.
    • e.g.

    • e.g.

    • For e.g.

    • e.g.

    • e.g.

    • e.g. 

    • e.g.  

  • Here are several pairs of expressions that are commonly mistaken to be identities.
    • Note that the bases are not the same.

    • Instead,

    • Recall that that is, the correct expansion contains terms such as .

    • Instead, . Note carefully where each minus sign appears.

    • But it is true that   .

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