The index, or exponent of a power is the number denoting the height, or degree of that power. Thus, 2 is the index of the 2nd power.
Powers that are to be raised, are usually denoted by placing the index above the root, or first power.
Thus 22 = 4, the 2nd power of 2.
Example.—What is the 2nd power of 45?
45 × 45 = 2025 Answer.
EVOLUTION.
Evolution is the reverse of Involution, being the extracting, or finding the roots of any given powers, or numbers.
The Root of any number, or power, is such a number as being multiplied into itself a certain number of times, will produce that power.
Thus, 2 is the square root, or 2nd root of 4, because, 22 = 2 × 2 = 4; and 3 is the cube root, or third root of 27. But there are many numbers of which a proposed root can never be exactly found; by means of decimals, however, the root may be very nearly ascertained.
Any power of a given number, or root, may be found exactly by multiplying the number continually into itself.