# Examples of power

### In mathematics

Power is the representation of the successive multiplication of a number by itself. It is a way of writing a product of a number by itself and the times that multiplication will be done. The exponent is the number of times to be multiplied.

Example :

2 is the power, which is equal to 5 x 5 .

The result is 25 .

Another example in reverse would be: 2 x 2 x 2 x 2 x 2 x 2 , whose representation is 6 .

There are also other types of this representation in mathematics:

• Power set: it is the set that integrates all possible subsets of a given set.
• Equipotence: given two sets A and B , they are equipotent between them if there exists a function from A in B such that for each element y of B , there exists exactly one element x of A such that f (x) = y.1.
• Power of a set: it is the set that is defined from the properties of the Cartesian product.
• Power point: the result that links the lengths of segments of straight lines passing through a die and cut to a fixed point circumference.
• Power of a test: statistical probability that the alternative hypothesis being true, rejects the null hypothesis.

### Examples of power in mathematics

• 2 = 4 x 4 = 16
• 3 = 3 x 3 x 3 = 27
• (−3) 2 = (−3) x (−3) = 9
• 0.5 2 = 0.5 x 0.5 = 0.25
• (2 2 ) -3 = 2 2x ( -3 ) = 2 6 = 1/2 6 = 1/64 (as a fraction, to eliminate the negative sign of the exponent)

In physics power is called the amount of work done by a body in a unit of time.

The formula is P = W / t , where W is work (in joules) and t is time (in seconds).

• In optics : it is the inverse of the focal length of a lens.
• Power stage: an audio amplifier.
• Acoustic power: it is the amount of energy emitted through sound waves per unit of time.
• Electrical power: amount of electrical energy that is transported in a unit of time. Its value is expressed in watts.
• Mechanics: it is the amount of force applied to a body as a function of the speed with which it is exerted. Its formula is P = F xv , where F is force and v is velocity.

### Examples of power in physics

• You want to lift a 90 kg piano to a seventh floor at a height of 15 meters. It takes 6 seconds for the lift to raise the piano. Calculate the power of the crane.

FORMULA: P = W / t. Where T is work, which must be calculated because it is unknown.

W = F xdx cos α = 90 x 9.8 x 15 x 1 = 13.230 N

So the power of the crane will be:

P = 13.230 / 6 = 2205 W

• Calculate the power dissipated by a 5 Ω resistor if a current of 5 A.

In this case, it is necessary to calculate the electrical power, for which the following formula is used:

FORMULA: P = R ∙ I 2

5 x 5 2 = 125 W.