College Algebra: Exponent Rules Flashcards

Questions and Answers

What is the Product Rule of exponents?

$(a^m)^n = a^{m*n}$

$a^m x a^n = a^{m+n}$ (correct)

$a^0 = 1$

$a^m/a^n = a^{m-n}$

What is the Quotient Rule of exponents?

$a^m x a^n = a^{m+n}$

$a^m/a^n = a^{m-n}$ (correct)

$(a^m)^n = a^{m*n}$

a^0 = 1

What is the Power Rule of exponents?

$a^m x a^n = a^{m+n}$

$(a^m)^n = a^{m*n}$ (correct)

$a^0 = 1$

$a^m/a^n = a^{m-n}$

What does the Zero Exponent Rule state?

$a^0 = 1$ Signup and view all the answers

How does the Negative Rule of exponents work?

$a^{-n} = 1/a^n$ Signup and view all the answers

What is the Power of a Product Rule?

$(ab)^m = a^m * b^m$ Signup and view all the answers

What does the Power of a Quotient Rule state?

$(a/b)^n = a^n/b^n$ Signup and view all the answers

What is a perfect square trinomial?

(x + a)^2 = x^2 + 2ax + a^2 Signup and view all the answers

What is the formula for the Difference of Squares?

$x^2 - y^2 = (x + y)(x - y)$ Signup and view all the answers

What is the formula for the Sum of Cubes?

$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ Signup and view all the answers

What is the formula for the Difference of Cubes?

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ Signup and view all the answers

What is an algebraic expression?

Constants and variables combined using addition, subtraction, multiplication, and division. Signup and view all the answers

Study Notes

Exponent Rules

Product Rule: For any base ( a ) raised to powers ( m ) and ( n ), the product is expressed as ( a^m \times a^n = a^{m+n} ).
Quotient Rule: When dividing like bases, such as ( a^m ) by ( a^n ), it simplifies to ( a^{m-n} ).
Power Rule: Raising a power to another power gives: ( (a^m)^n = a^{m \cdot n} ).
Zero Exponent Rule: Any base ( a ) (except zero) raised to the zero power equals one: ( a^0 = 1 ).
Negative Exponent Rule: Negative exponents indicate reciprocals, such that ( a^{-n} = \frac{1}{a^n} ).

Product and Quotient Rules

Power of a Product Rule: When multiplying two bases raised to the same power, it can be separated: ( (ab)^m = a^m \cdot b^m ).
Power of a Quotient Rule: For a fraction raised to a power, it can be split as follows: ( \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} ).

Polynomial Identities

Perfect Square Trinomial: The expansion of ( (x + a)^2 ) results in ( x^2 + 2ax + a^2 ).
Difference of Squares: The expression ( x^2 - y^2 ) can be factored into ( (x + y)(x - y) ).
Sum of Cubes: The formula ( a^3 + b^3 ) factors as ( (a + b)(a^2 - ab + b^2) ).
Difference of Cubes: The expression ( a^3 - b^3 ) factors into ( (a - b)(a^2 + ab + b^2) ).

Fundamental Algebra Concepts

Algebraic Expression: Consists of constants and variables linked by addition, subtraction, multiplication, and division to form mathematical statements.

Description

This quiz covers essential exponent rules including the Product Rule, Quotient Rule, and Power Rule. Ideal for students studying College Algebra using OpenStax materials. Test your understanding of these foundational concepts with this engaging flashcard quiz.