| Fundamentally, power is the rate of doing work.
Work is the product of force and the distance covered when the force is applied (F x d). So power is (F x d)/t, were t is time. We are
familiar with the forces of the number line. So what is the work done by these forces?
They operate on two or more occupants of the number line (operands) and produce results. The more the operands, the more the work. The more concise the
operations, the faster the operations produce results. Powers of the number line are the results of successive self-multiplications
with the general form x y , where x and y are greater than 1 (there is no significant self-multiplication in the case of x, y = 0 or 1).
The number x is called the base and y is called the power or exponent of the base .
Examples of power numbers are: 4 = 2 x 2 = 2 2 27 = 3 x 3 x 3 = 3 3 256 = 4 x 4 x 4 x 4 = 4 4 When the exponent is a negative number, the result is the reciprocal or inverse of the corresponding power number. For example, 2 -2 = 1/2 2 = 1/4. |
| When the exponent is a fraction, the result is called
the root of the base number .
Square roots (the exponent is 1/2) and
cube roots (the exponent is 1/3) are popular roots .
In general, the nth root of x is expressed as x 1/n ,
where 1/n is a fraction.
The following Exponent Rules are applicable for real numbers: a m x a n = a m + n . ( a m ) n = a m x n a m x b m = ( a b )m a 0 = 1 a 1 = a Power numbers are fundamental components of the structure of number systems. They also play important roles in various areas of applied mathematics. For example, the number of addresses in a 32 -address-pin Random Access Memory (RAM) is the power number, 2 32 . Peter O. Sagay |
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