If `(3/5)^3(3/5)^-6=(3/5)^(2x-1)`

If log_(e )k=2[(3)/(5)+(1)/(3)((3)/(5))^(3)+(1)/(5)((3)/(5))^(5)+….oo] then k =

-(3)/(5)times(3)/(5)+(5)/(2)-(3)/(5)times(1)/(6)

Solve : (x+3)/(7)-(3x-5)/(5)=(2x-5)/(3)-25

If l=int((2x-3)^(1/2))/((2x-3)^(1/3)+1)dx=3[(1)/(7)(2x-3)^(7/6)-(1)/(5)(2x-3)^(5/6)+(1)/(3)(2x-3)^(1/2)-(2x-3)^(1/6)+g(x)]+c then g(x) is equal to

Solve : (1)/(3)x-6=(5)/(2)

If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo then find 3x^(2)+6x.

The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1) (x+3)/3=(y-5)/1=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/5 (3) (x-3)/3=(y+5)/1=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/5

Show that 1 + 1/2.(3/5) + (1.3)/(2.4) (3/5)^2 + (1.3.5)/(2.4.6) (3/5)^3 + …… = sqrt([5/2])

Simplify and write the answer in the exponential form : (2^5-:2^8)^5"x"\ 2^(-5) (ii) \ (-4)^3"x"\ (5)^(-3)"x"\ (-5)^(-3) (iii) 1/8"x"\ 3^(-3)

Evaluate : a. (-1)^(11) b. (-3)^(2)xx(5)^(3) c. 6^(2)xx3^(3) d. (-2)^(3)xx(-5)^(2) e. (-1)^(7)xx2 f. (-1)^(4)xx(-1)^(5) g. 4^(3)xx3^(4) h. (-2)^(5)xx5^(3) i. (-4)^(3)xx(-6)^(3) j. (-1)^(33)xx(-3)^(1) k. ((-1)/(6))^(2) l. ((2)/(11))^(3)