# Powers And Exponents

Powers and Exponents are mathematical operations which can be written as x­n, this is known as power and here ‘x’ is the base and ‘n’ the exponent. Powers and exponents are basically same things. The exponent generally appears at the top right of the base in the superscript form. The exponentiation xn can be read as ‘x’ to the power ‘n’. Also some exponent terms have their pronunciation like x2 will be pronounced as ‘x square’ and x3 is pronounced as ‘x cube’. The reason behind these terminologies is that area of square with side ‘x’ will be x2 and the volume of cube with side ‘x’ will be x3.

They are widely used in the field of economics, biology, physics, chemistry and computer science they are also pervasive in nature. They can be used in calculation of population growth, compound interest, wave behavior.

The exponent describes that how many times the base will be multiplied by itself. For instance 53 = 5*5*5 = 125. The base 5 appears 3 times in the repeated multiplication because of the power of 3. More precisely here 5 is the base 3 is the exponent and 125 appears as the power and it will be pronounced as 5 to the power 3.

Exponents and powers may be generalized in the integers and integers can be broken down in more general types. These types are:

·         Positive integer exponent can be defined by the initial condition x1 = x and the recurrence relation will be xn+1 = xn. x and the associativity of multiplication will follow xr+t xr . xt.

·         Arbitrary integer exponent: For non-zero ‘q’ and positive ‘n’ the recurrence relation can be written as qn = q+ 1/q.

·         Any number whose power is 1 then result is number itself, it does not change.

·         Any nonzero number whose exponent is 0 then the outcome will be 1.

When the base is non zero than the following identities be used:

xr+t xr . xt,

x mn = x m.n,

(x.y)n = xn . yn,

This is all about exponents powers.

Math Topics