The expression 3b4c33 6b 1 a5 7 equals narbsct where hellip

The expression (3b^4c^3)^3 (6b^- 1 a^5)^- 7 equals na^rb^sc^t where hellip n, the leading coefficient, is: _________ r, the exponent of a is: ____________ s, the exponent of b is: ___________ and t, the exponent of c is: ____________

Solution

Solution:

Given that

(3b⁴c³)³ (6b^-1a⁵)^-7 = n a^r b^s c^t

LHS =Left hand side = (3b⁴c³)³ (6b^-1a⁵)^-7

  = 27 b^4x3 c^3x3 ( 6^-7 b^-1x(-7) a^5x(-7) ) .... { (A^B)^C = A^{BxC }}

= 27 b¹² c⁹ ( 1/(3x2)⁶ ) (b⁷ a^-35)

= 3³/(3⁶x2⁶) a ^-35 b¹²⁺⁷ c⁹

  = 1/(3³x2⁶) ( a^-35 b¹⁹ c⁹)

= 1/1728 ( a^-35 b¹⁹ c⁹)

1/1728 ( a^-35 b¹⁹ c⁹) =  n a^r b^s c^t

As we compare we get the following result

(i) n = 1/1728

(ii) r = -35

(iii) s= 19

(iv) t = 9

Answer