`((5)/(7))^(2)-:((5)/(7))^(3x+1)=((5)/(7))^(4)`

Find the sum of each of the following infinite geometric series, if it exists : (4)/(7) - (5)/(7^(2)) + (4)/(7^(3)) - (5)/(7^(4)) + (4)/(7^(5)) - (5)/(7^(6)) +…oo

(3x-4)/(7)+(7)/(3x-4)=(5)/(2)

(5+5+5)/(7+7+7)-(5+5)/(7+7)+(5)/(7)=?(1)/(7)(b)(3)/(7)(c)(5)/(7)(d)(13)/(14)

Simplify: ((1)/(4)x(2)/(7))-((5)/(14)x(-2)/(3))+((3)/(7)x(9)/(2))

Simplify: ((sqrt(2))/(5))^(8)-:((sqrt(2))/(5))^(13) (ii) ((5^(-1)x7^(2))/(5^(2)x7^(-7)))^((1)/(2))x((5^(-2)x7^(3))/(5^(3)x7^(-5)))^(-(5)/(2))

Simplify : (i) (5x - 9y) - (-7x + y) (ii) (x^(2) -x) -(1)/(2)(x - 3 + 3x^(2)) (iii) [7 - 2x + 5y - (x -y)]-(5x + 3y -7) (iv) ((1)/(3)y^(2) - (4)/(7)y + 5) - ((2)/(7)y - (2)/(3)y^(2) + 2) - ((1)/(7)y - 3 + 2y^(2))

If (x)/(y)=(6)/(5), then the value of ((6)/(7)-(5x-y)/(5x+y)) is equal to (a) (1)/(7)( b) (2)/(7)(c)(3)/(7) (d) (4)/(7)

Verify the following: (i) ((3)/(4)+(-2)/(5))+(-7)/(10)=(3)/(4)+((-2)/(5)+(-7)/(10)) (ii) ((-7)/(11)+(2)/(-5))+(-13)/(22)=(-7)/(11)+((2)/(-5)+(-13)/(22)) (iii) -1+((-2)/(3)+(-3)/(4))=(-1+(-2)/(3))+(-3)/(4)