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Questions and Answers
What does the Product Rule state?
What does the Product Rule state?
- Keep the base and subtract the exponents.
- Keep the base and add the exponents. (correct)
- Multiply the bases and keep the exponents.
- Change the base to zero.
What does the Quotient Rule describe?
What does the Quotient Rule describe?
- Keep the base and add the exponents.
- Change the base to one.
- Keep the base and subtract the smaller exponents from the larger exponents. (correct)
- Multiply the bases and keep the exponents.
According to the Power Rule, what happens when raising a power to a power?
According to the Power Rule, what happens when raising a power to a power?
- Subtract the exponents.
- Change the base to zero.
- Keep the base and add the exponents.
- Keep the base and multiply the exponents. (correct)
What is the Group of Factors rule?
What is the Group of Factors rule?
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What is the Power Rule for Quotients?
What is the Power Rule for Quotients?
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What do Negative Exponents tell you to do?
What do Negative Exponents tell you to do?
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What does factoring mean in mathematics?
What does factoring mean in mathematics?
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What are radicals?
What are radicals?
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What is a perfect square?
What is a perfect square?
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What is the Difference of Squares?
What is the Difference of Squares?
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Study Notes
Exponent Rules
- Product Rule: In multiplication involving the same bases, retain the base and add the exponents.
- Quotient Rule: In division with the same bases, keep the base and subtract the smaller exponent from the larger one.
- Power Rule: When a power is raised to another power, maintain the base and multiply the exponents.
- Group of Factors: Apply the power rule to each individual factor within a group.
Specific Power Rules
- Power Rule for Quotients: When applying the power rule to fractions, it must be applied to both the numerator and denominator.
- Negative Exponents: Indicates the use of the reciprocal; for example, a^-n = 1/a^n.
Fundamental Concepts
- Factoring: Involves breaking down numbers into factors that, when multiplied together, produce the original number.
- Radicals: Represent expressions involving roots such as square roots and cube roots.
- Perfect Square: A number created by squaring an integer, e.g., 1, 4, 9.
- Difference of Squares: Characterized by two squared terms separated by a subtraction, e.g., a^2 - b^2.
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