Mathematic power

A power is a compact way of writing repeated multiplication of the same number by itself. It is made up of two parts: a base, which is the number being multiplied, and an exponent (also called an index), a small number written to the upper right that tells you how many times the base is used as a factor. Powers grow astonishingly fast: raising a number to a larger exponent quickly produces enormous values, which is why we speak of "exponential" growth. A few special cases are worth remembering, such as any nonzero number raised to the power of zero being equal to one, and a power of one simply giving back the base itself. Exponents also make expressions far shorter and easier to handle, and they follow neat rules for multiplying, dividing, and nesting powers.

Powers are everywhere in mathematics and the world around us: they describe areas and volumes, appear in scientific notation for very large and very small numbers, drive compound interest and population growth, and underpin computing, where everything is built on powers of two. Understanding them is a stepping stone to roots, logarithms, and algebra as a whole.