Question

Consider a rational (i.e. "fractional") exponent...what does the denominator of the fractional exponent represent in radical form? What does the numerator of the fractional exponent represent?

Do the normal rules of exponents (i.e. the product, quotient, and power rules) apply to fractional exponents? What are some of the unique challenges presented in using these rules with fractional exponents? Give an example to make your point.