5.1 Integer Exponents
Product Rule
Quotient Rule
Power Rules (2 different ones)
Negative exponents
(for any )
Scientific Notation
8.1 Radical Expressions
Find roots
Graph radical functions
may help to find a root using your calculator (or for different problems in 8.2)
8.2 Rational Exponents
Remember the rule:
Use it to write exponentials as radicals
Use it also to write radicals as exponentials
8.3 Simplifying Radicals
Product Rule
Quotient Rule
Rules for simplifying radicals:
1. no fractions in radicand
2. no radicals inside a denominator
3. the index and any exponents in the radicand must have no common factor greater
than 1
4. the radicand must have no factor raised to a power
the index
8.4 Add/subtract radicals
Simplify each radical first, then treat any common radicals like a variable when you add/subt.
When fractions are involved, try to simplify each fraction, then add/subt. using the LCD
8.5 Multiply/”Divide” Radicals
FOIL binomials
To “divide” rationalize the denominator
When the denominator is a binomial, multiply the numerator and denom. by the
conjugate.
8.6 Solving Equations with Radicals
Isolate one radical
Use the power rule
Solve the new equation
Check EVERY possible solution in ORIGINAL equation
8.7 Complex Numbers
Use i to multiply, divide, and simplify radical expressions
Add/subtract complex numbers (combine like terms)
Multiply complex numbers (FOIL)
“Divide” complex numbers (use complex conjugate to get i out of the denominator)
Find different powers of i