Properties of Exponents

Exponents, also known as powers, are a way of expressing repeated multiplication. Here are some of the key properties of exponents:

1. Product of Powers Property: When you multiply two powers that have the same base, you can add the exponents. For example, a^m * a^n = a^(m+n).

2. Quotient of Powers Property: When you divide two powers that have the same base, you can subtract the exponents. For example, a^m / a^n = a^(m-n).

3. Power of a Power Property: When you raise a power to another power, you can multiply the exponents. For example, (a^m)^n = a^(m*n).

4. Zero Exponent Property: Any non-zero number raised to the power of zero is 1. For example, a^0 = 1.

5. Negative Exponent Property: A number with a negative exponent can be rewritten as the reciprocal of the number with the positive exponent. For example, a^-m = 1/a^m.

6. Power of a Product Property: When a product is raised to a power, each factor is raised to that power. For example, (ab)^m = a^m * b^m.

7. Power of a Quotient Property: When a quotient is raised to a power, both the numerator and the denominator are raised to that power. For example, (a/b)^m = a^m / b^m.

These properties can be used to simplify expressions involving exponents.