Rules of Exponents

Step-by-step to find the Rules of Exponents

The following rules are the most commonly used exponent’s rules:

1. Product of powers: When multiplying two numbers with the same base, add the exponents. For example, \((a^m)(a^n) = a^{(m+n)}\)
2. Quotient of powers: When dividing two numbers with the same base, subtract the exponent of the denominator from the exponent of the numerator. For example, \((a^m)/(a^n) = a^{(m-n)}\)
3. Power of a power: When raising a number with an exponent to another power, multiply the exponents. For example, \((a^m)^n = a^{(mn)}\)
4. Power of a product: When raising a product of numbers to a power, raise each factor to that power. For example, \((ab)^n = a^n * b^n\)
5. Power of a quotient: When raising a quotient of numbers to a power, raise the numerator and denominator to that power. For example,\((\frac{a}{b})^n\) \(=\frac{a^n}{b^n}\)
6. Zero power: any nonzero number raised to the power of zero is \(1\), for example, \(a^0 = 1\)
7. Negative exponent: When a number is raised to a negative exponent, it is equivalent to the reciprocal of the number raised to the positive exponent. For example, \(a^{-n} =\frac{1}{a^n}\)
8. Exponent of \(1\): any nonzero number raised to the power of \(1\) is the number itself, for example \(a^1 = a\)