Understanding the Mathematics of Personal Finance

EXPONENTS

An exponent is another neat notation. Suppose I want to multiply an expression by itself (called “squaring” the expression):

(j + 7)0 + 7) = (j + 7)2.

The little “2” placed high up in the upper right means “square the expression” or more directly, “write the expression down twice, making it clear that you mean multiplication.” This is also sometimes called “raising the expression to the power of 2. ”

Similarly, I can “cube” the expression

(j + 7)0 + 7)0 + 7) = (j + 7)3

and so on.

In general, (anything)" is called raising the expression “anything” to the nth power.

The following discussion of exponents is not needed in order to understand the book; I just thought that some readers might be curious as to why raising an expres­sion to the power of 2 is called “squaring the expression” and raising it to the power of 3 is called “cubing the expression.”

The area inside a rectangle is calculated by multiplying the rectangle’s length by its width. A square is a rectangle whose length is equal to its width. In other
words, all four sides of a square are the same length. The area of a square is therefore calculated by taking the square ’ s length (or width) and multiplying it by itself. Consequently multiplying a number by itself is called “squaring” and raising a number to the second power is just multiplying the number by itself. Incidentally, if you start with the area of a square and want to find the length of its sides, the procedure is called “finding the square root.”

Similarly, all the edges of a cube are the same, and consequently, you find the volume of the cube by “cubing,” that is, raising the length of any edge to the third power.

It’s also possible to raise expressions to “non-integer” powers, for example,

(j + 7)25.

This cannot be explained without the use of logarithms, which is a topic that is beyond what you need to understand this book. I will use this notation when I have to calculate, for example, 2.5 years’ worth of interest on a loan. Your calculator or spreadsheet will handle this correctly; you don’t need to worry about it.

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