English Medium Class 9 - CBSE Question Bank Solutions

Simplify the following:

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

Simplify the following

`((4xx10^7)(6xx10^-5))/(8xx10^4)`

Simplify the following

`(4ab^2(-5ab^3))/(10a^2b^2)`

Simplify the following

`((x^2y^2)/(a^2b^3))^n`

Simplify the following

`(a^(3n-9))^6/(a^(2n-4))`

If a = 3 and b = -2, find the values of :

a^a + b^b

If a = 3 and b = -2, find the values of :

a^b + b^a

If a = 3 and b = -2, find the values of :

(a + b)^ab

Prove that:

`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`

Prove that:

`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`

Prove that:

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

Prove that:

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

Prove that:

`(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc`

Prove that:

`(a^-1+b^-1)^-1=(ab)/(a+b)`

If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`

Simplify the following:

`(3^nxx9^(n+1))/(3^(n-1)xx9^(n-1))`

Simplify the following:

`(5xx25^(n+1)-25xx5^(2n))/(5xx5^(2n+3)-25^(n+1))`

Simplify the following:

`(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)`

Simplify the following:

`(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)`

Solve the following equation for x:

`7^(2x+3)=1`