Powers

Powers is a term that appears in several domains with overlapping but distinct meanings. In mathematics, it denotes exponentiation; in physics and engineering, it refers to the rate of doing work; in politics and law, it concerns authority and governance. In popular culture, "powers" often describes supernatural or extraordinary abilities.

In arithmetic and algebra, a power is written as a^n, where a is the base and n the exponent. It means multiplying the base by itself n times. For example, 3^4 = 3×3×3×3 = 81. Rules include (ab)^n = a^n b^n and a^{mn} = (a^m)^n. Negative and fractional exponents correspond to reciprocals and roots.

In physics, power is the rate at which energy is transferred or work is performed. It is measured in watts, where one watt equals one joule per second. Power depends on force and speed (P = F·v), and it is central to devices from light bulbs to engines and power plants; efficiency relates powered output to input energy.

In governance, power denotes the capacity to influence or control resources and people. Political theory discusses the distribution of powers among branches of government, a concept known as separation of powers. Powers can be delegated, reserved, or devolved, and are subject to legal limits and checks and balances.

In fiction and popular culture, characters may possess superpowers or extraordinary abilities. The word derives from the Latin potens meaning powerful, with related terms like potency and potential.