Question

Part 1: Explain, in complete sentences, how multiplying and dividing factors with rational exponents is similar to multiplying and dividing factors with integer exponents. Part 2: Give one example of multiplying factors with rational exponents. Part 3: Give one example of multiplying factors with integer exponents.

Answer 1

The rules for multiplying factors with integer exponents is x^m * x^n = x^(m+n)
The rules for dividing factors with integer exponents is x^m/x^n = x^(m-n).

The rules are the same if the exponents are rational numbers such as a/b or c/d
Example x^1/2 * x ^1/3 = x^5/6. The only difference is that you must insure erac exponent has a common denominator.

x^2 * x^4 = x^6

x^1/6 * x ^1/12 = x^1/4