How To: Simplify exponential expressions via the quotient rule

Simplify exponential expressions via the quotient rule

This video demonstrates the quotient rule as applied to exponential expressions that appear in the form of, to use the word loosely, a fraction. The name, "quotient rule", refers to the fact that it applies to expressions which are divided by other expressions. The video begins by explaining that the quotient rule allows expressions in this form to be simplified if they contain like bases (i.e., the terms are of the same variable). The quotient rule allows the expression to be simplified by simply subtracting the exponential powers of each term in the division. The video goes on to demonstrate the truth of the quotient rule by expanding the exponents of both the dividend term and the divisor term; this yields a more intuitive approach to the mathematical workings of the quotient rule. The first example involves exponents of the variable, "X", and it is solved with the quotient rule. Next, a different case is presented in which the bases of the terms are the number "5" as opposed to a variable; none the less, the quotient rule applies in the same way. Finally, a third case is demonstrated in which one of the terms in the expression contains a negative exponent.

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