8^(x+1)=16^(y+2)" and "((1)/(2))^(3+x)=((1)/(4))^(3y)

Solve the following equations: (i) 3^(x+1)=27 xx 3^4 (ii)4^(2x)=(16 3)^(-6/y)=(sqrt(8))^2 (iii) 3^(x-1) xx 5^(2y-3)=225 (iv) 8^(x+1)=16^(x+2) and, (v) (1/2)^(3+x)=(1/4)^(3y) 4^(x-1) xx (0. 5)^(3-2x)=(1/8)^x sqrt(a/b)=(b/a)^(1-2x ) , where a , b are distinct positive primes.

Solve the following simultaneous equations. (1)/(3x + y) + (1)/(3x - y) = (3)/(4) , (1)/(2(3x + y)) - (1)/(2(3x - y)) = - (1)/(8)

Solve the following system of equations: (1)/(3x+y)+(1)/(3x-y)=(3)/(4),quad (1)/(2(3x+y))-(1)/(2(3x-y))=-(1)/(8)

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

(1)/(2(3x+4y))=(1)/(5(2x-3y))=(1)/(4),

The equation of the ellipse having a vertex at (6,1) a focus at (4,1) and the eccentricity (3)/(5) is 1) ((x-1)^(2))/(16)+((y-1)^(2))/(25)=1 (2) ((x-1)^(2))/(25)+((y-1)^(2))/(16)=1 3) ((x+1)^(2))/(25)+((y+1)^(2))/(16)=1 (4) ((x+1)^(2))/(16)+((y+1)^(2))/(25)=1

(1) / (3x + y) + (1) / (3x-y) = (3) / (4) (1) / (2 (3x + y)) - (1) / (2 (3x-y) )) = - (1) / (8)

If x^(3)-2x^(2)y^(2)+5x+y-5=0 and y(1)=1, then (a y'(1)=(4)/(3)(b)y'(1)=-(4)/(3)(c)y''(1)=-8(22)/(27) (d) y'(1)=(2)/(3)