`(2^2 xx 3^2 )/(2^(-2)) xx 3^(-1)`

Simplify and express each of the following as a rationla number . ((1)/(2))^(3) xx (( 3)/(2))^(2) xx 2^(3)

Simplify : 2^2xx(3^2/2^-2)xx3^-1

Simplify: (2^-1xx2)/(2^2xx3^-4)^(7/2) xx (2^-2xx3^2)/(2^3xx3^-5)^(-5/2)

Evaluate each of the following: (i)\ (2/(11))^4\ xx\ \ ((11)/3)^2\ xx\ \ (3/2)^3 (ii)\ (1/2)^5\ xx\ ((-2)/3)^4xx\ (3/5)^(-1)

Show that, (1 xx 2^(2) + 2 xx 3^(2) + ….+ n xx (n+1)^(2))/(1^(2) xx 2 + 2^(2) xx 3 + ….+ n^(2) xx (n+1))= (3n+ 5)/(3n+ 1)

Show that (1 xx 2^(2) + 2 xx 3^(2) + ... +n xx (n + 1)^(2))/(1^(2) xx 2 + 2^(2) xx 3+ ... + n^(2) xx (n + 1)) = (3n + 5)/(3n + 1)

Show that (1 xx 2^(2) + 2 xx 3^(2) + . . . + n xx ( n + 1) ^(2))/( 1 ^(2) xx 2 + 2^(2) xx 3 + . . . + n^(2) xx ( n + 1) ) = ( 3 n + 5)/( 3 n + 1 )

The sum (3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) + (7 xx (1^(3) + 2^(3) + 3^(3)))/(1^(2) + 2^(2) + 3^(2)) + ....

The sum (3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) + (7 xx (1^(3) + 2^(3) + 3^(3)))/(1^(2) +2^(2) + 3^(2))... upto 10th term is

The sum up to 10 terms of the series (3 xx 1^(3))/(1^(2)) + (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) + (7 xx (1^(3) + 2^(3) + 3^(3)))/(1^(2) + 2^(2) + 3^(2)) + ....