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Distributive Rule
ab+ac = a(b+c)
ab-ac = a(b-c)
Multiply Exponents
x4x3 = x(3+4) = x7
Divide Exponents
x8/x5 = x(8-5) = x3
Exponent raised to an exponent
(x3)2 = x(2*3) = x6
Negative Exponents
x-2 = 1/x2
0^0?
Undefined
Any nonzero number to the zero power equals?
1.

50 = 1
Any number to the first power equals?
Itself.

51 = 5
One to any power equals?
1.

134 = 1
Zero to any nonzero power equals?
0.  Zero.

034 = 0
When you raise a number between 0 and 1, to a positive power, what do you get?

aka "The Zone"
...a smaller number.

(1/2)*(1/2) = 1/4
A negative number raised to an odd power is...
...negative.

(-2)3 = -2
A negative number raised to an even number is...
...positive.

(-2)4 = 16
Scientific Notation
7.8x105 = 780,000
2.3x10-4 = 0.00023
Roots
Study square roots of numbers. Know how to multiply them together, divide them, rationalize the denominator...

√16 = +4
but...
x2 = √16
x = ±4

When you take the root of a number between 0 and 1, you get a larger number.
How do you add or substract roots?
The number under the radicals has to be identical.

√3 + 5√3 = 6√3
How do you multiply roots?
a√r x b√s = ab√(r x s)
How do you divide roots?
√(x/y) = (√x)/(√y)
What are Fractional Exponents?
Fractional Exponents are really roots.

271/3 = 3√27 = 3
Quadratics
-Know how to multiply two terms to create a quadratic equation.
-Know how to FOIL (First, Outside, Inside, Last)
-The roots of an equation are the solutions.
-To find the roots of a quadratic, move all terms to one side and leave 0 on the other side. Quadratic must equal zero. Factor the polynomial. Set each of the factors equal to zero and solve.
(x+y)2 = ...
= x2 + 2xy + y2
(x-y)2 = ...
= x2 -2xy + y2
(x+y)(x-y) = ...
= x2 - y2
Factorials
n! = n(n-1)(n-2)(n-3)(n-4)...(1)

8! = 8x7x6x5x4x3x2x1 = 40320

What is 12!/11!? 12 because everything cancels.

0! = 1! = 1
√25 = ?
+25 (NOT -25!)

3√-8 = -2
xy < 0
means that x and y have opposite signs.
x of y cards