The properties of exponents are rules that simplify expressions involving powers. One key property is the product of powers, which states that when multiplying two expressions with the same base, you add their exponents: a^m × a^n = a^(m+n). Another important rule is the power of a power, where you multiply the exponents when raising a power to another power: (a^m)^n = a^(m*n) . Additionally, the quotient of powers property indicates that when dividing two expressions with the same base, you subtract the exponents: a^m ÷ a^n = a^(m-n) . Lastly, any non-zero base raised to the power of zero equals one: a^0 = 1. These properties help in simplifying and solving exponential equations.