one

x⁰ = 1

5⁰ = 1

129⁰ = 1

base x base

or base²

the reciprocal of something

x^-4 = ^1⁄(x⁴)

add the exponents

x³ × x² = x(³⁺²) = x⁵

True or False?

You can multiply unlike bases

False

Ex: dogs cannot multiply with Cats

to divide like bases

subtract the exponents

x^{5 ÷} x² = x(^{5 - 2}) = x³

True or False?

You cannot add or subtract like bases with different exponents.

True

the bases and exponents must be the same for you to add or subtract the terms.

True or False?

You cannot simply add or subtract the numerical coefficients of unlike bases.

True

Like working with cats and dogs, they don't mingle

numbers greater than 1, and cannot be divided other than by 1 and themselves.

Examples:

2, 3, 5, 7, 11, and 13

numbers that can be divided other than by 1 or themselves.

Examples:

4, 6, 8, 9, 10, and 12.

Follow these steps:

1. Isolate the variable, which means getting all the x's on one side and all non-x's on the other side.

2.  Add all the x's on one side; add all the non-x's on the other side.

3.  Divide both sides of the equation by the number in front of the x.

First, Outer, Inner, Last and refers to the order in which you multiply variables in parantheses.

(a + b) (a - b) =

1. First:  a × a = a²

2. Outer: a × (-b) = -ab

3. Inner: b × a = ba (the same as ab)

4. Last: b × (-b) = -b²

add like terms: -ab + ab +0ab

final solution: a² - b²

First FOIL problem to memorize

(a + b)² = a² + 2ab + b²

final solution

a² + 2ab + b²

Second FOIL problem to memorize

(a - b) ² = a² - 2ab + b²

Final solution

a^{2 -} 2ab + b²

Third FOIL problem to memorize

(a - b) (a + b) = a² - b²

Final Soution

a² - b²