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Bases and Exponents (rules)
operations to add, multiply, divide bases and exponents
19
Mathematics
Graduate
07/03/2009

Additional Mathematics Flashcards

 


 

Cards

Term
the base is
Definition
the big number, or letter on the bottom
Term
the exponent is
Definition
the little number, or letter in the upper-right corner
Term
A base to the zero power always equals
Definition

one

x0 = 1

50 = 1

1290 = 1

Term
A base to the second power is
Definition

base x base

or base2

Term
A base to a negative exponent is
Definition

the reciprocal of something

x-4 = 1⁄(x4)

Term
to multiply like bases
Definition

add the exponents

x3 × x2 = x(3+2) = x5

Term

True or False?

You can multiply unlike bases

Definition

False

Ex: dogs cannot multiply with Cats

Term

 

to divide like bases

Definition

subtract the exponents

x5 ÷ x2 = x(5 - 2) = x3

Term
a numerical coefficient is
Definition
the number in front of the base
Term

True or False?

You cannot add or subtract like bases with different exponents.

 

Definition

True

 

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

Term

True or False?

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

Definition

True

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

Term
prime numbers are
Definition

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

Examples:

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

Term
composite numbers are
Definition

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

Examples:

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

Term
Solving for x
Definition

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.

Term
FOIL Method
Definition

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

Term

First FOIL problem to memorize

(a + b)2 = a2 + 2ab + b2

Definition

final solution

a2 + 2ab + b2

Term

Second FOIL problem to memorize

(a - b) 2 = a2 - 2ab + b2

Definition

Final solution

a2 - 2ab + b2

Term

Third FOIL problem to memorize

(a - b) (a + b) = a2 - b2

Definition

Final Soution

a2 - b2

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