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Questions and Answers
What are exponents also called?
What are exponents also called?
What does the base represent in an exponentiation expression?
What does the base represent in an exponentiation expression?
The number or letter with the exponent.
What is an expression in mathematics?
What is an expression in mathematics?
A collection of monomials attached by addition or subtraction.
What is an equation?
What is an equation?
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To combine bases with different exponents, you can just ______________ the exponents together.
To combine bases with different exponents, you can just ______________ the exponents together.
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What is the result of simplifying a⁵a²?
What is the result of simplifying a⁵a²?
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What is the simplified form of (3x²y)(6x³y²)?
What is the simplified form of (3x²y)(6x³y²)?
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What are the steps for evaluating an expression?
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?
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?
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!
