d -5) and we get +20; then multiply the means together (-4X) and the extremes together (-5X) and add (-4X + -5X) = -9X. Place together in descending order: - + 20. There is a grouping we should recognize by inspection in the generic type of (X2 - K2), which factors into (X - K)(X + K). Here are several examples: (X2 - 1), which factors into (X + 1) (X - 1) or X2 - 64, which factors into +8)(X - 8). Adding and Subtracting Exponents. An exponent is a number at the right of and above a symbol. The value assigned to the symbol with this number is called a power of the symbol, although power is sometimes used in the same sense as exponent. If the exponent B.3 INTRODUCTORY ALGEBRA is a positive integer and X denotes the symbol, then xn means x if n = 1. When n > 1, 31 = 32=9,3 = 27, and SO on. Note that x° = 1 if X itself is not zero. Rules: When we multiply, we add exponents; when we divide, we subtract exponents. For the zero example above, we can think of it as X2/X2 = X0 = 1. This addition and subtraction can be carried out SO long as there is a common base. In this case it was X. For example, 23 X 22 = 25. Another example: = Because it is division, we subtracted exponents; it had the common base "x" A negative exponent indicates, in addition to the operations indicated by the numerical value of the exponent, that the quantity is to be made a reciprocal. Example 1: 4-2 = =1/16. Example 2: X - 3 1/X 3. Furthermore, when addition is involved, and the numbers have a common exponent, we can just add the base numbers. For example, 3.1 x 10-10 + 1.9 X 10-10 = X 10-10 We cannot do this if there is not a common base and exponent. The power of 10 is used widely throughout the text. If the exponent is a simple fraction such as 1/2 or 1/3, then we are dealing with a root of the symbol or base number. For example, 91/2 = 3. Or (X2 + 2X + 1/2 = X + 1. Carry this one step further. Suppose we have x2/3. First we square X and then take the cube root of the result. The generalized case is XP/q = in other words, we first take the pt