3 Questions
Which property states that the product of powers with the same base is equal to the base raised to the sum of the exponents?
Product of Powers
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?
Power of a Quotient
Which property allows us to write a negative exponent as the reciprocal of the base raised to the positive exponent?
Negative Exponent
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.
Test your knowledge on the properties of rational exponents with this quiz. Learn how to simplify expressions with rational exponents using the product, power, quotient, and negative exponent rules. Discover how these rules are similar to integral exponents and how they can be applied to solve problems. With examples provided, this quiz will help you sharpen your skills in working with rational exponents.
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