Podcast
Questions and Answers
What is the Product Rule?
What is the Product Rule?
When you multiply two powers that have the same base, you can add the exponents.
What is the Quotient (Division) Rule?
What is the Quotient (Division) Rule?
When you divide two exponents with the same base, you keep the base and subtract the powers.
What does the Zero Exponent Rule state?
What does the Zero Exponent Rule state?
Any base (except 0) raised to the zero power is equal to one.
What is the Power Rule?
What is the Power Rule?
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Explain the Expanded Power Rule.
Explain the Expanded Power Rule.
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What happens with Negative Exponents?
What happens with Negative Exponents?
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What is the Power of Fraction Rule?
What is the Power of Fraction Rule?
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Study Notes
Exponent Rules in Mathematics
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Product Rule: When multiplying powers with identical bases, add the exponents. For example, ( a^m \times a^n = a^{m+n} ).
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Quotient Rule: When dividing powers with the same base, maintain the base and subtract the exponents. For example, ( \frac{a^m}{a^n} = a^{m-n} ).
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Zero Exponent Rule: Any base (excluding zero) raised to the power of zero equals one. For example, ( a^0 = 1 ) (unless ( a = 0 ), where ( 0^0 ) is considered undefined).
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Power Rule: When raising a power to another power, the base remains the same while the exponents are multiplied. For example, ( (a^m)^n = a^{m \times n} ).
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Expanded Power Rule: Similar to the Power Rule, but emphasizes that if an exponent is outside parentheses, it applies to everything inside. Distribute the exponent through all terms in the parentheses.
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Negative Exponents: Moving a factor across the fraction bar changes the sign of the exponent. For example, ( a^{-n} = \frac{1}{a^n} ). Important notes: ( -x ) is not equal to ( \frac{1}{x} ), and ( a^{-1} \neq 1/a ) if ( a = 0 ).
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Power of Fraction Rule: This rule outlines how to handle fractional bases raised to exponents, focusing on applying the exponent to both the numerator and denominator separately when needed.
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Description
Test your knowledge of exponent rules with these flashcards designed for 7th grade math. You'll learn about the Product Rule, Quotient Rule, and Zero Exponent Rule. This quiz will help reinforce your understanding of essential exponent concepts.
