Intermediate algebra introduces fractional exponents as a topic of study. Fractional exponents are often used during algebraic manipulation and calculus operations, such as integration and differentiation, to alleviate the necessity for using radicals. This often makes operations simpler for students who are more familiar with exponents. Fractional exponents must, in the end, be changed back into radicals to show that all simplifications have been made. The intimate relationship between radicals and exponents allows for this process to be done mechanically.
Instructions
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1
Place the quantity raised to a fractional exponent underneath a radical symbol.
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2
Place the denominator of the fractional exponent in the upper left corner of the radical symbol. This number reflects the index of the radical.
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3
Raise the quantity under the radical symbol to the number found in the numerator of the fractional exponent. As an example, 5 ^ 3/2 = √(5)^3 = √125. Note, that when no index is given on a radical symbol it is assumed to have an index equal to two.