Edmentum Plato Algebra II Unit 1 Vocab Test
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Questions and Answers

What does $a^m x a^n = a^{m+n}$ represent?

  • Sum of powers
  • Difference of powers
  • Quotient of powers
  • Product of powers (correct)
  • What does $(ab)^m = a^m x b^m$ represent?

  • Product of powers
  • Power of a sum
  • Power of a product (correct)
  • Power of a quotient
  • What does $(a^m)^n = a^{mn}$ represent?

  • Quotient of powers
  • Power of a power (correct)
  • Product of powers
  • Negative exponent
  • What does $a^m / a^n = a^{m-n}$ represent?

    <p>Quotient of powers</p> Signup and view all the answers

    What is the property represented by $(a/b)^m = a^m / b^m$?

    <p>Power of a quotient</p> Signup and view all the answers

    What is $w^2 + 5w$?

    <p>Expression</p> Signup and view all the answers

    In the expression $w^2 + 5w$, what is the variable?

    <p>w</p> Signup and view all the answers

    In the expression $w^2 + 5w$, what is the exponent of 'w'?

    <p>2</p> Signup and view all the answers

    In the expression $w^2 + 5w$, what is the coefficient of the variable term?

    <p>5</p> Signup and view all the answers

    What are the terms in the expression $w^2 + 5w$?

    <p>w^2 and 5w</p> Signup and view all the answers

    What are algebraic expressions?

    <p>Groups of symbols such as numbers, variables, and operators.</p> Signup and view all the answers

    The value of an algebraic expression depends on what?

    <p>The value of its variables.</p> Signup and view all the answers

    What is any base with an exponent of 0?

    <p>1</p> Signup and view all the answers

    What is a zero exponent?

    <p>A base raised to the power of zero is equal to 1.</p> Signup and view all the answers

    What is a negative exponent?

    <p>A nonzero base raised to a negative exponent is equal to the reciprocal of the base raised to a positive exponent.</p> Signup and view all the answers

    The distributive property is true for what?

    <p>All real numbers.</p> Signup and view all the answers

    What are like terms?

    <p>Terms that have the exact same variables raised to the exact same powers.</p> Signup and view all the answers

    What does the commutative property allow?

    <p>It allows us to put like terms together and combine them.</p> Signup and view all the answers

    What is factoring?

    <p>The process of writing an expression in terms of a product of factors.</p> Signup and view all the answers

    What is a quadratic?

    <p>A relationship in which the highest power of the unknown quantity is the second power.</p> Signup and view all the answers

    The solution to a one-variable linear equation is the value of the ______________ that makes the equation true.

    <p>variable</p> Signup and view all the answers

    What is the reflexive property?

    <p>a = a</p> Signup and view all the answers

    What is the symmetric property?

    <p>If a = b and b = c, then a = c.</p> Signup and view all the answers

    Study Notes

    Exponents and Properties of Powers

    • Product of Powers: ( a^m \times a^n = a^{m+n} )
    • Power of a Product: ( (ab)^m = a^m \times b^m )
    • Power of a Power: ( (a^m)^n = a^{mn} )
    • Quotient of Powers: ( \frac{a^m}{a^n} = a^{m-n} )
    • Power of a Quotient: ( \left( \frac{a}{b} \right)^m = \frac{a^m}{b^m} )

    Algebraic Expressions and Components

    • An algebraic expression consists of numbers, variables, and operators, excluding relational signs like "=".
    • Variables are letters representing unknown quantities (e.g., "w" in ( w^2 + 5w )).
    • Exponents indicate the power to which a variable is raised (e.g., "2" in ( w^2 + 5w )).
    • Coefficients are the numerical factors in terms (e.g., "5" in ( 5w )).
    • Terms are individual parts of an expression (e.g., ( w^2 ) and ( 5w ) in ( w^2 + 5w )).

    Key Properties

    • Any base raised to an exponent of zero equals one (e.g., ( a^0 = 1 )).
    • A nonzero base raised to a negative exponent equals the reciprocal of the base raised to a positive exponent.
    • The distributive property holds for all real numbers, allowing distribution across addition or subtraction.
    • Like terms share identical variable components raised to the same powers, differing only in coefficients.

    Mathematical Properties

    • Commutative Property: Facilitates combining like terms by changing their order.
    • Reflexive Property: States ( a = a ), affirming equality.
    • Symmetric Property: If ( a = b ) and ( b = c ), then inevitably ( a = c ).

    Special Types of Expressions

    • Factoring is rewriting an expression as a product of its factors.
    • Quadratics are expressions where the highest power of the variable is two (e.g., ( ax^2 + bx + c )).
    • The solution to a one-variable linear equation defines the variable's value that satisfies the equation's condition.

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    Test your understanding of key vocabulary terms in Algebra II with this flashcard quiz. Each card covers essential properties of exponents and powers, helping solidify your understanding of the unit's concepts.

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