Questions and Answers
What are exponents also called?
What does the base represent in an exponentiation expression?
The number or letter with the exponent.
What is an expression in mathematics?
A collection of monomials attached by addition or subtraction.
What is an equation?
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To combine bases with different exponents, you can just ______________ the exponents together.
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What is the result of simplifying a⁵a²?
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What is the simplified form of (3x²y)(6x³y²)?
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What are the steps for evaluating an expression?
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Evaluate the expression 5x² - 6y - 4z given x=5, y=3, z=-2. What is the result?
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Evaluate the expression 6x + 2xy + 4z³ given x=5, y=3, z=-2. What is the result?
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Study Notes
Exponents
- Represent repeated multiplication and are denoted by superscripts.
- Examples:
- ( x^2 = x \times x )
- ( bc^3 = b \times c \times c \times c )
- ( y^4 = y \times y \times y \times y )
- ( 6h^5 = 6 \times h \times h \times h \times h \times h )
- Like terms require matching variables and exponents.
Base
- The number or variable that is raised to a power in exponential expressions.
Expression
- A collection of monomials linked by addition or subtraction.
- Lacks an equal sign and can only be simplified, not solved.
Equation
- Similar to expressions, but often includes an equal sign to show equality.
Multiplying Exponents
- When multiplying the same base with different exponents, add the exponents.
- Example: ( (x^5)(x^4) = x^{5+4} = x^9 )
Simplifying Exponents
- To simplify expressions with the same base, add the exponents.
- Example: ( a^5a^2 = a^{5+2} = a^7 )
Example of Multiplying Expressions
- For ( (3x^2y)(6x^3y^2) ):
- ( x^2 \times x^3 = x^5 )
- ( y \times y^2 = y^3 )
- Coefficients: ( 3 \times 6 = 18 )
- Overall result: ( 18x^5y^3 )
Steps for Evaluating Expressions
- Identify given values for variables.
- Substitute these values into the expression.
- Follow the order of operations to simplify.
Evaluating Expressions Example 1
- For ( 5x^2 - 6y - 4z ) with ( x=5, y=3, z=-2 ):
- Calculation: ( 5(5^2) - 6(3) - 4(-2) )
- Result: ( 125 - 18 + 8 = 115 )
Evaluating Expressions Example 2
- For ( 6x + 2xy + 4z^3 ) with ( x=5, y=3, z=-2 ):
- Expansion: ( 6(5) + 2(5)(3) + 4(-2^3) )
- Calculation of ( -2^3 = -8 )
- Result: ( 30 + 30 - 32 = 28 )
Additional Examples
- More examples on simplifying and evaluating expressions available for practice.
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Description
This quiz explores algebraic expressions with a focus on exponents and their evaluation. Understand how exponents represent repeated multiplication through various examples. Test your knowledge with this informative flashcard set!
