English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

If `a=xy^(p-1), b=xy^(q-1)` and `c=xy^(r-1),` prove that `a^(q-r)b^(r-p)c^(p-q)=1`

Assuming that x, y, z are positive real numbers, simplify the following:

`(sqrt(x^-3))^5`

Assuming that x, y, z are positive real numbers, simplify the following:

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

Assuming that x, y, z are positive real numbers, simplify the following:

`(x^((-2)/3)y^((-1)/2))^2`

Assuming that x, y, z are positive real numbers, simplify the following:

`(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))`

Assuming that x, y, z are positive real numbers, simplify the following:

`root5(243x^10y^5z^10)`

Assuming that x, y, z are positive real numbers, simplify the following:

`(x^-4/y^-10)^(5/4)`

Assuming that x, y, z are positive real numbers, simplify the following:

`(sqrt2/sqrt3)^5(6/7)^2`

Simplify:

`(16^(-1/5))^(5/2)`

Simplify:

`root5((32)^-3)`

Simplify:

`root3((343)^-2)`

Simplify:

`(0.001)^(1/3)`

Simplify:

`((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))`

Simplify:

`(sqrt2/5)^8div(sqrt2/5)^13`

Simplify:

`((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)`

Prove that:

`sqrt(3xx5^-3)divroot3(3^-1)sqrt5xxroot6(3xx5^6)=3/5`

Prove that:

`9^(3/2)-3xx5^0-(1/81)^(-1/2)=15`

Prove that:

`(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=16/3`

Prove that:

`(2^(1/2)xx3^(1/3)xx4^(1/4))/(10^(-1/5)xx5^(3/5))div(3^(4/3)xx5^(-7/5))/(4^(-3/5)xx6)=10`

Prove that:

`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`