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.
5 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 2 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
- 4 2 = 4 x 4 = 16
- 3 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.