ICSE ICSE Class 8 - CISCE Question Bank Solutions for Mathematics

Simplify:

`(36"x"^2)^(1/2)`

Simplify:

`(125"x"^-3)^(1/3)`

Simplify:

`(2"x"^2"y"^-3)^-2`

Simplify:

`(27"x"^-3"y"^6)^(2/3)`

Simplify:

`(-2"x"^(2/3)"y"^(-3/2))^6`

Simplify and express as positive indice:

`("a"^(-2)"b")^(1/2)xx("a""b"^-3)^(1/3)`

Simplify and express as positive indice:

(xy)^(m-n).(yz)^(n-l).(zx)^(l-m)

Show that:

`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`

Evaluate:

`(x^(5+n)(x^2)^(3n+1))/x^(7n-2)`

Evaluate:

`("a"^(2"n"+1)xx"a"^((2"n"+1)(2"n"-1)))/("a"^("n"(4"n"-1))xx("a"^2)^(2"n"+3)`

Prove that:

`("m"+"n")^-1("m"^-1+"n"^-1)=("m""n")^-1`

Prove that:

`((x^a)/x^b)^(1/(ab))((x^b)/x^c)^(1/(bc))(x^c/x^a)^(1/(ca))=1`

Prove that:

`1/(1+"x"^("a"-"b"))+1/(1+"x"^("b"-"a"))=1`

Find the value of n, when:

`12^-5xx12^(2"n"+1)=12^13÷12^7`

Find the value of n, when:

`("a"^(2"n"-3)xx("a"^2)^("n"+1))/(("a"^4)^-3)=("a"^3)^3÷("a"^6)^-3`

Simplify:

`("a"^(2"n"+3)."a"^((2"n"+1)("n"+2)))/(("a"^3)^(2"n"+1)."a"^("n"(2"n"+1)`

Simplify:

`("x"^(2"n"+7).("x"^2)^(3"n"+2))/"x"^(4(2"n"+3)`

Mohit sold a T.V. for Rs. 3,600; gaining one-sixth of its selling price. Find :
(i) the gain
(ii) the cost price of the T.V.
(iii) the gain percent.

By selling a certain number of goods for Rs. 5,500; a shopkeeper loses equal to one-tenth of their selling price. Find:

1. the loss incurred
2. the cost price of the goods
3. the loss as a percent.

A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :
(i) its cost price;
(ii) the loss percent.