# Rules of Exponents

The rules of exponents are a set of mathematical operations that can be performed on numbers with exponents. Some of the most commonly used exponent's rules are described in this article.

## Step-by-step to find the Rules of Exponents

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

- Product of powers: When multiplying two numbers with the same base, add the exponents. For example, \((a^m)(a^n) = a^{(m+n)}\)
- 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, \((a^m)/(a^n) = a^{(m-n)}\)
- Power of a power: When raising a number with an exponent to another power, multiply the exponents. For example, \((a^m)^n = a^{(mn)}\)
- Power of a product: When raising a product of numbers to a power, raise each factor to that power. For example, \((ab)^n = a^n * b^n\)
- Power of a quotient: When raising a quotient of numbers to a power, raise the numerator and denominator to that power. For example,\((\frac{a}{b})^n\) \(=\frac{a^n}{b^n}\)
- Zero power: any nonzero number raised to the power of zero is \(1\), for example, \(a^0 = 1\)
- 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, \(a^{-n} =\frac{1}{a^n}\)
- Exponent of \(1\): any nonzero number raised to the power of \(1\) is the number itself, for example \(a^1 = a\)

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