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.

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.

cwrw238 · Answer

denominator = root
numerator = power

eg   x ^ (3/2)  = sqrt(x^3)

cwrw238 · Answer

normal rules of exponents do apply

cwrw238 · Answer

as for the challenges - there is no problem if you know the rules of adding,subtracting, multiplying and dividing fractions