Section 1
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exponential form
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Cards (55)
Section 1
(50 cards)
exponential form
a number written with a base and an exponent
Power of a Product Property
To find a power of a product, find the power of each factor and multiply
Associative Property of Multiplication
Changing the grouping of three or more factors does not change the product.
Sets
a collection of items called elements
radical symbol
the symbol √ used to denote a root
constant term
a term that has a number but no variable
empty set/null set
is a set containing no elements
Additive Inverse Property
The sum of a number and its opposite is zero.
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself.
Zero Exponent Property
Any number, except for zero, taken to the zero power is equal to 1.
Quotient of Powers Property
to divide powers with the same base, subtract the exponents
subset
is a set whose elements all belong to another set
Quotient Property of Square Roots
the square root of a quotient is equal to the quotient of the square roots of the dividend and the divisor
Multiplicative Inverse Property
The product of any number and its multiplicative inverse (its reciprocal) is one
interval
set of all numbers between two endpoints (i.e. between 3 and 5)
set-builder notation
uses the properties of the elements in the set to define the set
order of operations
the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction
Distributive Property of Multiplication
the property that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products
Closure Property of Multiplication
the product of two real numbers is a real number 2(3)=6
Power of a Power Property
to raise one power to another, multiply the exponents
roster notation
a way of representing a set by listing the elements between braces
irrational numbers
Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.
interval notation
A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval. [ ] used to include an endpoint in an interval ( ) used to exclude an endpoint from an interval
like radical terms
square roots that have the same radicand
whole numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Closure Property of Addition
the sum of two real numbers is a real number 2+3=5
Integers
whole numbers and their opposites
Natural Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbers.
like terms
terms with exactly the same variable factors in a variable expression
Product of Powers Property
to multiply powers with the same base, add the exponents
infinite set
a set with an unlimited, or infinite, number of elements
unlike radicals
Radical expressions that do not have the same radicands.
method of representing intervals
use of inequality symbols
The Density Property
the property that states that between any two real numbers, there is always another real number
Additive Identity Property
The sum of any number and zero is the number
Commutative Property of Addition
Changing the order of the addends does not change the sum.
rational number
Any number that can be expressed as a ratio (quotient) of two integers, where the denominator is not zero
Multiplicative Identity Property
The product of any number and one is the number
Base of a power
the number or expression that is used as a factor in a repeated multiplication
Radicand
The number or expression inside (under) a radical symbol
Commutative Property of Multiplication
Changing the order of the factors does not change the product.
Product Property of Square Roots
the square root of a product is equal to the product of the square roots of the factors
Negative Exponent Property
A nonzero base raised to a negative exponent is equal to the reciprocal of the base raised to the opposite, positive exponent
principal root
the positive square root of a number
Associative Property of Addition
Changing the grouping of three or more addends does not change the sum.
Elements
a collection of items in a set
rationalizing the denominator
a method used to eliminate radicals from the denominator of a fraction
finite set
a set with a definite, or finite, number of elements
methods of set notation
roster notation, interval notation, and set-builder notation
Coefficient
number in front of a variable
Section 2
(5 cards)