Algebraic Properties and Expressions Flashcards

Questions and Answers

What does the exponent in an expression indicate?

How many times to multiply the base number by itself (correct)

The value of the base number

How many times to add the base number

The number of terms in the expression

What is the term for a number that appears beneath the exponent?

Base

Define an exponential expression.

An expression that involves an exponent.

What does PEMDAS stand for?

Parentheses, Exponent, Multiply/Divide, Add/Subtract Signup and view all the answers

What are variables?

Symbols representing unknown or changeable values Signup and view all the answers

What separates terms in algebraic expressions?

<ul> <li>or - signs</li> </ul> Signup and view all the answers

What are coefficients?

Numbers that multiply variables. Signup and view all the answers

What are like terms?

Terms that have the same variables raised to the same powers. Signup and view all the answers

What is the distributive property?

The rule that a(b + c) = ab + ac. Signup and view all the answers

What are radical expressions?

Expressions that contain one or more radical signs. Signup and view all the answers

What are radicands?

The numbers under the radical signs. Signup and view all the answers

What is a radical in mathematics?

The symbol √ used to indicate a square root. Signup and view all the answers

Study Notes

Algebraic Properties and Expressions

Exponent: Indicates how many times to multiply the base by itself. Example: In 2^3, the exponent is 3, so 2 * 2 * 2 = 8.
Base: The main number in an exponential expression that is raised to a power. Example: In 2^3, the base is 2.
Exponential Expression: Contains an exponent and may include variables. Example: 4x^3 translates to 4 * x * x * x.
PEMDAS: Acronym for the order of operations:
- P: Parentheses
- E: Exponent
- MD: Multiply/Divide
- AS: Add/Subtract
Variables: Symbols (often lowercase, italicized) representing unknown or changeable values. Example: In 4x - 5y = 9, x and y are variables.
Terms: Components of algebraic expressions separated by + or - signs, which may include numbers, variables, or both. Example: In 5x^2 + 2x + 7, the terms are 5x^2, 2x, and 7.
Algebraic Expressions: Mathematical phrases that include one or more variables. A numerical expression contains no variables. Example: p - 4 is an algebraic expression with variable p.
Coefficients: Numbers that multiply the variables in a term. Example: In -7x, -7 is the coefficient; in y, the coefficient is 1.
Like Terms: Terms that share the same variable and exponent. Example: 5ab and -22ab are like terms; 8x^2 and 6x are not due to differing exponents.
Distributive Property: Allows multiplication over addition or subtraction; if a, b, and c are expressions, then a(b + c) = ab + ac. Example: 5(x + 2) = 5x + 10.
Radical Expressions: Math expressions containing radical signs (sqrt) indicating roots.
Radicands: The numbers found under the radical sign in radical expressions.
Radical: Symbol (√) representing square roots or (ⁿ√) for nth roots. Example: √3 indicates the square root of 3, approximately equal to 1.732.

Description

Test your knowledge of algebraic properties and expressions with these flashcards. Each card features key terms such as exponent and base, along with their definitions and examples. Perfect for students needing a quick review or preparation for exams.