Exponent

Positive exponents

The associativity of multiplication implies that for any positive integers m and n, when multiplying exponentiation results with the same base b and exponents m and n, the product is the same base b to the power of the sum m + n of the exponents: $${\displaystyle b^{m+n}=b^{m}\cdot b^{n},}$$ and, when taking the result of exponentiation to another power, the base remains the same, and the exponents multiply: $${\displaystyle (b^{m})^{n}=b^{mn}.}$$