Questions and Answers
What is the property of exponents that expresses a power raised to another power?
What is the Division Property of Exponents?
The Division Property of Exponents states that when dividing two powers with the same base, you subtract the exponents.
What is the Multiplication Property of Exponents?
The Multiplication Property of Exponents states that when multiplying two powers with the same base, you add the exponents.
Define the Zero Exponent Property.
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What does the Power of a Quotient Property of Exponents state?
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Explain the Power of a Product Property of Exponents.
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What is the Negative Exponent Property?
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Study Notes
Power of a Power Property of Exponents
- When raising a power to another power, multiply the exponents.
- Example: ((a^m)^n = a^{m \cdot n})
Division Property of Exponents
- When dividing two powers with the same base, subtract the exponents.
- Example: (\frac{a^m}{a^n} = a^{m-n})
Multiplication Property of Exponents
- When multiplying two powers with the same base, add the exponents.
- Example: (a^m \cdot a^n = a^{m+n})
Zero Exponent Property
- Any non-zero base raised to the power of zero equals one.
- Example: (a^0 = 1) (where (a \neq 0))
Power of a Quotient Property of Exponents
- When raising a quotient to a power, apply the exponent to both the numerator and denominator.
- Example: (\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n})
Power of a Product Property of Exponents
- When raising a product to a power, apply the exponent to each factor in the product.
- Example: ((ab)^n = a^n \cdot b^n)
Negative Exponent Property
- A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent.
- Example: (a^{-n} = \frac{1}{a^n}) (where (a \neq 0))
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Test your understanding of exponent rules with these flashcards designed for pre-algebra. Each card covers a different property of exponents, helping you master the foundational concepts necessary for algebra. Perfect for quick reviews and memorization.