What does it mean when one says that a rational exponent represents both an integer exponent and the root? What if the rational exponent is 3/3?

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crmhaske | College Teacher | (Level 3) Associate Educator

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In a rational exponent the numerator represents the integer exponent, and the denominator represents the root.  For 3/3:


Following the rules of exponents, you can easily simplify this expression to equal x because (3)(1/3)=1.

This is how you end up with rational exponents in the first place.  The exponent of the root of a function is 1/root.  Therefore, when you multiply an integer exponent to a root exponent you end up with (integer)(1/root)=(integer/root).

To illustrate with another example:


Following the rules of exponents that state that a variable to the exponent m raised to the exponent n equals the variable to the power of m times n


We get: