Question

Properties of Exponents

Answer 1

1. Multiplication Property: When two numbers with the same base are multiplied, you can add the exponents.
Example: \(a^m \cdot a^n = a^{m+n}\)
2. Division Property: When two numbers with the same base are divided, you can subtract the exponents.
Example: \(\frac{a^m}{a^n} = a^{m-n}\)
3. Power of a Power Property: When a number with an exponent is raised to another exponent, you can multiply the exponents.
Example: \((a^m)^n = a^{m \cdot n}\)
4. Power of a Product Property: When a product is raised to an exponent, you can distribute the exponent to each factor.
Example: \((ab)^n = a^n \cdot b^n\)
5. Negative Exponent Property: Any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent.
Example: \(a^{-n} = \frac{1}{a^n}\)
6. Zero Exponent Property: Any number raised to the power of zero is equal to 1.
Example: \(a^0 = 1\)
7. Fractional Exponent Property: An exponent that is a fraction indicates a root.
Example: \(a^{\frac{1}{n}} = \sqrt[n]{a}\)