Literal Numbers & Power of literal numbers

Literal Numbers
We have mentioned earlier that the letters represent the numbers. These letters are called literal numbers and obey all the rules of arithmetic. 
Note :  5 × p × q = 5pq. 5, p and q are factors of 5pq. 5 is a numerical factor and p, q are literal factors.

Power of literal numbers 
We have read earlier that 2 x 2 x 2 = 2³ and (–3) x (– 3) = (–3)²      Similarly, a x a x a = a³ and (– y) x (– y) x (– y)  x (– y) = (–y)⁴ 
a³ is read as 'a to the power three' or 'a raised to the power three' or 'a cube' or 'third power of a' and (–y)⁴ is read as '–y to the power four' or '–y raised to the power four' or fourth power of –y'. 
In a³, a is called base and 3 is called exponent or index. 

Coefficient
The number expressed in figures or symbols, standing before an algebraic term as a multiplier is called its coefficient. Thus in 3abc, 3 is the coefficient of abc, 3a is the coefficient of bc and 3ab is the coefficient of c. 

Ex.1     Write down the coefficient of :
(a) x in 3xy    (b) abc in – 5abc     (c) y in 2xyz   (d) a² in – a²bc 

Sol.     (a) 3y             (b) – 5            (c) 2xz             (d) – bc 

Ex.2 Write down the numerical coefficient in each of the following :
           (a) 5 ab         (b) – 3xyz      (c) px          (d) –y 
Sol.    (a) 5              (b) –3            (c) 1            (d) – 1 

Ex.3     If a = 2, b = 3, c = 4, find the value of : 
           (a)     3a – b + 2c 
           (b)     a² – b² + c²        
           (c)     ab – 3abc – 2ac 

Sol.    (a)     3a – b + 2c = 3 x 2 – 3 + 2 x 4 = 6 – 3 + 8 = 11 
          (b)     a² – b² + c²  = 2² – 3² + 4² = 4 – 9 + 16 = 11 
         (c)     ab – 3abc – 2ac = 2 x 3 – 3 x 2 x 3 x 4 – 2 x 2 x 4 = 6 – 72 – 16 = – 82