How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents?

Question

 Theres really nothing else to this i simply wish to know the answer to the question above. thank you

Answer 1

I recommend replacing every radical [e.g. n^th root of a monomial] by said monomial to the 1/n power.

 

Working with fractional exponents VASTLY simplifies most of the classical exercises that one finds in an Algebra book. Use of fractional exponents becomes a vital algebraic skill in Calculus.

 

The concept of rationalizing a denominator can be treated in the following way: Said irrationality stems from the fact that the exponents in a monomial are fractional; the act of rationalizing the denominator becomes simply the act of multiplying both top & bottom of the quotient by whatever power needed to bring the exponent up to the next integer.  [E.g. 1 over cube root of x needs multiplication of numerator & denominator by x to the two thirds.]