Definition
Law of exponents
A law of exponents is a rule that rewrites powers without changing their value.
What it means
An exponent counts repeated factors. When powers share the same base, some operations let you combine those counts: multiplying adds exponents, dividing subtracts them, and a power of a power multiplies them. Choose the law that matches the operation; addition does not use these rules.
Remember it
Same base first; then combine exponent counts by the operation’s law.
Example
Simplify 5³ × 5². The base is the same, so add the exponents: 5³ × 5² = 5³⁺² = 5⁵ = 3,125. Three factors of 5 followed by two more make five factors of 5.
Watch for
2³ + 2² is 8 + 4 = 12, not 2⁵. A product law does not turn addition into exponent addition.
Common mix-up
Do not add the bases: 3² × 3⁴ becomes 3⁶, not 6⁶.
Exact meaning
A law of exponents is an identity for powers, such as multiplying or dividing powers with the same base or raising a power to a power, used only under its stated conditions; division rules require a nonzero base.