As an expert in the field of physics and mathematics, I can provide a comprehensive definition of power that encompasses both disciplines.

Step 1: English Definition

In physics, power is defined as the rate at which work is done or energy is transferred or transformed. It is a fundamental concept that quantifies the amount of work done per unit time. When an object is moved over a distance by a force, work is said to be done on that object. Power is the measure of how quickly this work is performed. It is a scalar quantity and is typically measured in watts (W), where one watt is equivalent to one joule per second (J/s). The concept of power is crucial in understanding the operation of engines, electric motors, and various other machines that convert energy from one form to another.

The formula for power in physics is given by:

\[ P = \frac{W}{t} \]

where \( P \) is the power, \( W \) is the work done, and \( t \) is the time taken to do the work.

In mathematics, the term "power" refers to the operation of exponentiation. It is a mathematical process where a number, called the base, is multiplied by itself a certain number of times, which is indicated by an exponent. The exponent is a superscript number placed to the right and above the base. For example, \( 2^3 \) means that the base, 2, is multiplied by itself three times (i.e., \( 2 \times 2 \times 2 \)).

The general formula for a power in mathematics is:

\[ a^n = a \times a \times \cdots \times a \]

where \( a \) is the base and \( n \) is the exponent, indicating the number of times the base is multiplied by itself.

Powers are also used in various mathematical contexts such as complex numbers, where they can represent rotations and dilations in the complex plane, and in algebraic expressions where they can denote the degree of a polynomial.

Step 2: Divider

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power definition. In physics, the amount of energy put out or produced in a given amount of time. Power is often measured in watts or kilowatts. In mathematics, a power is a number multiplied by itself the number of times signified by an exponent placed to the right and above it.read more >>