base

The base is the number that is being multiplied by itself in a power. In 2^5 the base is 2 — it is the “thing” you keep multiplying, while the exponent up top says how many copies to use.

Writing b^n, we call b the base and n the exponent. The base can be any number (or even a variable or a whole expression), and changing it changes the size of the result dramatically: 2^10 is 1024, but 3^10 is 59049. Keeping track of exactly what the base is matters, because exponent rules only let you combine powers that share the same base.

Watch the sign carefully. In -2^4 the base is just 2 and the minus is applied afterward, giving -(2^4) = -16; you must write (-2)^4 to make -2 the actual base, which gives +16. This small notational trap catches many learners.