College Algebra: Exponent Rules Flashcards

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.

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.