`x^5-:(x^2xxy^2)xxy^3`

Simplify and express each of the following in exponential from: {(3^2)^3xx2^6}xx5^6 (ii) (x/y)^(12)xxy^(24)xx(2^3)^4

State True or False : x^(m)xxy^(m)=(x xxy)^(2m) , where x and y are non zero rational numbers and m is a positive integer.

If 21168=x^(4)xxy^(3)xxz^(2) , find (x+y+z)^((y+z)/(x+y)) , where x, y and z are positive integers.

The integral int(2x^(12)+5x^(9))/([x^(5)+x^(3)+1]^(3))*dx is equal to- (A) (x^(10))/(2(x^(5)+x^(3)+1)^(2))(B)(x^(5))/(2(x^(5)+x^(3)+1)^(2))(C)-(x^(10))/(2(x^(5)+x^(3)+1)^(2))(D)-(x^(5))/(2(x^(5)+x^(3)+1)^(2))

Factorisation by grouping the terms: (x^(2)+3x)^(2)-5(x^(2)+3x)-y(x^(2)+3x)+5y

The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to: (1)(-x^(5))/((x^(5)+x^(3)+1)^(2))+C(2)(x^(5)x^(3))/(2(x^(5)+x^(3)+1)^(2))+C(3)(x^(5))/(2(x^(5)+x^(3)+1)^(2))+C(4)(-x^(3)+x^(3))/(2(x^(5)+x^(3)+1)^(2))+C where C is an arbitrary constant.

x^(2)-3x=5(2-x)