Questions and Answers
What does $a^m x a^n = a^{m+n}$ represent?
What does $(ab)^m = a^m x b^m$ represent?
What does $(a^m)^n = a^{mn}$ represent?
What does $a^m / a^n = a^{m-n}$ represent?
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What is the property represented by $(a/b)^m = a^m / b^m$?
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What is $w^2 + 5w$?
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In the expression $w^2 + 5w$, what is the variable?
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In the expression $w^2 + 5w$, what is the exponent of 'w'?
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In the expression $w^2 + 5w$, what is the coefficient of the variable term?
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What are the terms in the expression $w^2 + 5w$?
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What are algebraic expressions?
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The value of an algebraic expression depends on what?
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What is any base with an exponent of 0?
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What is a zero exponent?
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What is a negative exponent?
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The distributive property is true for what?
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What are like terms?
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What does the commutative property allow?
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What is factoring?
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What is a quadratic?
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The solution to a one-variable linear equation is the value of the ______________ that makes the equation true.
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What is the reflexive property?
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What is the symmetric property?
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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.
Studying That Suits You
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Description
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.
