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Questions and Answers
Which property states that the product of powers with the same base is equal to the base raised to the sum of the exponents?
Which property states that the product of powers with the same base is equal to the base raised to the sum of the exponents?
- Quotient of Powers
- Product of Powers (correct)
- Power of Power
- Power of a Product
What is the property that states that the power of a quotient is equal to the quotient of the base raised to the power of the numerator and the denominator?
What is the property that states that the power of a quotient is equal to the quotient of the base raised to the power of the numerator and the denominator?
- Product of Powers
- Power of a Quotient (correct)
- Quotient of Powers
- Power of Power
Which property allows us to write a negative exponent as the reciprocal of the base raised to the positive exponent?
Which property allows us to write a negative exponent as the reciprocal of the base raised to the positive exponent?
- Negative Exponent (correct)
- Quotient of Powers
- Power of Power
- Power of a Quotient
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Study Notes
- Rational exponents have properties similar to integral exponents.
- 𝑎 and 𝑏 are positive real numbers and 𝑚 and 𝑛 are rational numbers.
- Product of Powers: 𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
- Power of Power: (𝑎𝑚)𝑛 = 𝑎𝑚𝑛
- Power of a Product: (𝑎𝑏)𝑚 = 𝑎𝑚𝑏𝑚
- Quotient of Powers: 𝑎𝑚/𝑎𝑛 = 𝑎𝑚−𝑛, 𝑎 ≠ 0
- Power of a Quotient: (𝑎/𝑏)𝑚 = 𝑎^𝑚/𝑏^𝑚, 𝑏 ≠ 0
- Negative Exponent: 𝑎^−𝑚 = 1/𝑎^𝑚, 𝑎 ≠ 0
- These properties are useful in simplifying expressions with rational exponents.
- The examples provided illustrate how to apply these properties in practice.
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