Viewing page 38 of 91

This transcription has been completed. Contact us with corrections.

21                   ARMY AIR FORCES

b. In algebra, because of the use of x as a letter, new signs are adopted to indicate multiplication.
(1) 4x means 4 times x. When no sign appears between letters and numbers, multiplication is indicated.
(2) 4 • x means 4 times x. When some sign of multiplication is necessary, a dot is used as indicated.
(3) In any product such as the foregoing, the coefficient of the x term is defined to be the rest of that term.
(4) When there is a product of the type x•x•x•x, it is written x⁴. The 4 is called the exponent of x, and x⁴ is called a power of x. This is simply a shorthand method of writing a product. The x is termed the base. 
Example: What are the coefficients and exponents of- 
4x²?  x²?  4x?  x? 
Solution:
4 is the coefficient and 2 is the exponent.
1 is the understood coefficient and 2 is the exponent.
4 is the coefficient and 1 the understood exponent.
1 is understood as the coefficient and exponent. 
c. Rules for use of exponents.
(1) When two powers with the same base are multiplied together, the exponents are added, as shown in the following illustrations:

3²•3³=3⁵=243
(9•27=243)
x²•x⁴=x⁶

(2) When two powers with the same base are divided, the exponents are subtracted, as the following examples show:

2⁵/2²=2³=8
(32/4=8)
x⁷/x³=x⁴

(3) When two products are multiplied together, the coefficients are multiplied and each power is multiplied separately, as in the following examples:
(a) 2x•3x²=6x³.
(b) 2abx•5a²x=10a³bx².
d. Terms are products or quotients separated from each other
                  
36