1. Passport to Advanced Mathematics Lessons 1-2
*Integer Exponents and Rules for Operations
*Radicals and Fractional Exponents
*Operations on Terms with Radicals
*Simplifying Rational Expressions
*Adding and Subtracting Polynomial Expressions with
Rational Coefficients
*Dividing Polynomials Expressions with Rational
Coefficients
*Adding and Subtracting Rational Expressions
*Multiplying and Dividing Rational Expressions

2. Integer Exponents and Rules for Operations
When multiplying variables – add the exponents
When dividing variables – subtract the exponents
When raising an exponent to a power – multiply the two exponents together
Expressions in parentheses raised to a power – pass the exponent out to all pieces
Negative exponents – move to the other side of the fraction
Numbers can follow these rules if treated as a base – don’t change the base

3. Radicals and Fractional Exponents
A fractional exponent is really power/root
Without a calculator – find the root first and then use the power
With a calculator – type it in as is
When rooting variables you actually divide the exponent on the variable by the index (root)
If it does not divide evenly, then the remaining variables stay in the radical sign

4. Operations on Terms with Radicals
Before you can add or subtract radicals you must first simplify them and make the radicand as small as possible
Then you treat them like variables and only add/subt the ones that look alike
You actually add/subt the real numbers in front, the radicals do not change
When multiplying or dividing, you use outside numbers with outside numbers and inside numbers with inside numbers
Clean up the radical before stopping

5. Simplifying Rational Expressions
Factor both the numerator and the denominator
Cancel exact binomials if they appear in the top and bottom
Cancel opposite binomials if they appear top and bottom, but insert (-1)
Reduce outside numbers and outside letters from the top and bottom
Never cancel top with top or bottom with bottom

6. Adding and Subtracting Polynomial Expressions with Rational Coefficients
Only add/subt like pieces
The variables remain the same and you add/subt the coefficients
When adding fractions without a calculator - you need a common denominator
When adding decimals without a calculator – remember to line up the decimal points verically

7. Dividing Polynomial Expressions with Rational Coefficients
Remember to divide each piece of the polynomial by the monomial in the denominator
Remember to divide letters means to subtract the exponents

8. Adding and Subtracting Rational Expressions
Factor the denominators
Identify the least common denominator
Rewrite the fractions over the new denominator
Add/Subt the numerators – remembering to only add like pieces
Leave the denominator the same
Factor the numerator of the answer to see if the fraction will reduce

9. Multiplying and Dividing Rational Expressions
Factor all numerators and all denominators that can be factored
Start reducing top pieces with bottom pieces
Cancel matching binomials
Cancel opposite binomials, insert (-1)
Reduce outside numbers
Reduce outside letters
**Never break up Binomials!!
Multiply remaining pieces – top x top and bottom x bottom
Check to see if you can reduce again