[" Simplify the following "],[[" (i) "3(a^(4)b^(3))^(10)times5(a^(2)b^(2))^(3)," (i) "(2x^(2)y^(3))," (c) "((4x)(1)^(2))/(8times10^(4))],[" (iv) "(4ab^(2)(-5ab^(3)))/(10a^(2)b^(2))," (w) "((x^(2)y^(2))/(a^(2)b^(3)))^(4)]]

Simplify that: (4ab^(2)(-5ab^(3)))/(10a^(2)b^(2))

Simplify the following: (6) (i) (a^(3)b^(2)c-ab^(3)c)-(3abc^(3)-a^(3)b^(2)c)-(4ab^(3)c+2abc^(3))

Simplify using following identiy: (a +- b) (a^(2) ab + b^(2)) = a^(3) +- b^(3) (2x + 3y) (4x^(2) - 6xy + 9y^(2))

Write each of the following in exponential form: a^(2)b^(3)xa^(3)b( ii) 3a^(2)b^(3)x 2ab^4 4x^(2)y^(3)x3xy^(2)x5x^(2)y

a^(2)b^(3)x2ab^(2) is equal to: 2a^(3)b^(4)(b)2a^(3)b^(5)(c)2ab (d) a^(3)b^(5)

Find each of the following products: (i) 5a^(2) b^(2) xx (3a^(2) - 4ab + 6b^(2)) (ii) (-3x^(2)y) xx (4x^(2) y - 3xy^(2) + 4x - 5y)

If (x)/(y)=(1)/(3), then (x^(2)+y^(2))/(x^(2)-y^(2))=?(a)-(10)/(9) (b) (5)/(4)(c)-(5)/(4)(d)-(5)/(3)

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is