Find n if :
a. `(3^(4))^(5)=(3^(2))^(n)`
b. `5^(12)=125^(n)`
c. `7^(2n+4)xx7^(4)=(7^(8))^(2)`
d. `8^(6)=64^(n)`

Find n if : a. ((4)/(49))^(5)xx((4)/(49))^(n-3)=((2)/(7))^(16) b. ((5)/(7))^(12)xx[((7)/(5))^(2)]^(8)=((7)/(5))^(2n-6) c. ((9)/(25))^(4)xx((9)/(25))^(n)=((3)/(5))^(12) d. ((3)/(5))^(20)xx[((5)/(3))^(3)]^(6)=((3)/(5))^(3n-13)

Simplify : a. [(3^(3))xx3^(4)]-:3^(4) b. 18^(6)-:3^(12) c. [(5^(6))^(9)xx(5^(15))^(5)]-[(5^(13))^(5)xx(5^(4))^(16)] d. (3^(5)xx10^(5)xx25)-:(5^(7)xx6^(5)) e. ((2)/(b))^(18)xxb^(12)xx(3^(4))^(3) f. [(2^(4))^(2)xx2^(12)]-:4^(2) g. 12^(8)-:3^(6) h. [(7^(7))^(8)xx(7^(9))^(5)]-[(7^(11))^(6)xx(7^(7))^(5)] i. (25^(2)xxp^(4)xxq^(8))-:(5^(3)xxp^(4)xxq^(7)) j. ((a)/(3))^(24)xx2^(8)xx(3^(6))^(4)

Find the value of n : (2^(3)xx5^(n+1)xx10^(2)xx5^(n-1))/(125xx5^(n-2)xx2^(7))=(25)/(4)

Find n such that (2/3)^3xx(2/3)^5=(2/3)^n^(-2) ((125)/8)^5xx((125)/8)^n=(5/2)^(18)

If .^(n)C_(5) = .^(n)C_(7) , then find .^(n)P_(3)

lim_(nrarroo) (3.2^(n+1)-4.5^(n+1))/(5.2^(n)+7.5^(n))=

Find the following sums : (i) .^(n)C_(0)-.^(n)C_(2)+.^(n)C_(4)-.^(n)C_(6)+"....." (ii) .^(n)C_(1)-.^(n)C_(3)+.^(n)C_(5)-.^(n)C_(7)+"...." (iii) .^(n)C_(0)+.^(n)C_(4)+.^(n)C_(8)+.^(n)C_(12)+"....." (iv) .^(n)C_(2) + .^(n)C_(6) + .^(n)C_(10)+.^(n)C_(14)+"......" (v) .^(n)C_(1) + .^(n)C_(5)+.^(n)C_(9)+.^(n)C_(13)+"...." (vi) .^(n)C_(3) + .^(n)C_(7) + .^(n)C_(11) + .^(n)C_(15) + "....."

Prove that (.^(n)C_(0))/(1)+(.^(n)C_(2))/(3)+(.^(n)C_(4))/(5)+(.^(n)C_(6))/(7)+"....."+= (2^(n))/(n+1)

Find the sum (1^4)/(1xx3)+(2^4)/(3xx5)+(3^4)/(5xx7)+......+(n^4)/((2n-1)(2n+1))

Simplify the following: (i)\ (5^(n+3)-\ 6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2\ xx\ 5^n) (ii)\ (6(8)^(n+1)+\ 16(2)^(3n-2))/(10(2)^(3n+1)-7\ (8)^n)