Exponents and Surds

If $\sqrt{2048}=\sqrt{2^{\mathrm{x}}},\sqrt{2187}=\sqrt{3^{\mathrm{y}}}$ and  $\sqrt{3125}=\sqrt{5^z}$ then the value of $x+y-z=$

If $5^{x+1}+5^{2-x}=126$, then $x$ is equal to

If x, y and z are positive real numbers and a, b and c are rational numbers, then value of $\frac{1}{1+x^{b-a}+x^{c-a}}+\frac{1}{1+x^{a-b}+x^{c-b}}+\frac{1}{1+x^{b-c}+x^{a-c}}$

  The roots of the equation $5^{x+1}+5^{2-x}=5^3+1$ will be _____. 

Value of ${\left(125\right)}^{\frac{1}{3}}.{\left(32\right)}^{\frac{1}{5}}$ will be

The value of $\left(\sqrt[2010]{2\sqrt{7}-3\sqrt{3}}\right)\left(\sqrt[4020]{55+12\sqrt{21}}\right)$ is

If $\sqrt{5+\sqrt[3]{x}}=3$, then the value of $x$ is 

If ${81}^y=\frac{1}{{27}^x}$, then the value of $x$ in terms of $y$ is

Of which number is $10608049$ a square ?

If $a, b$ and $c$ are integers such that $\left(\sqrt[3]{4}+\sqrt[3]{2}-2\right)\left(\sqrt[3]{4a}+\sqrt[3]{2b}+c\right)=20$ , then which one of the following is true?

The number of digits in $2^{120}\times 5^{124}$ is 

If  $\sqrt{x^2+\sqrt[3]{x^4{y}^2}}+\sqrt{y^2+\sqrt[3]{x^2{y}^2}}=K,$ then which of the following is true?

Simplify $\sqrt{\frac{48}{81}}$.

Simplify $\frac{\sqrt{12}}{\sqrt{3}}$

The ${100}^{th}$ root of ${10}^{\left({10}^{10}\right)}$ is

If ${25}^{x-1}=5^{2x-1}-100,$ then the value of $x$ is

$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$ equals

The fraction $\frac{2(\sqrt{2}+\sqrt{6})}{3\left(\sqrt{2+\sqrt{3}}\right)}$ is equal to

Value of $\sqrt[4]{(81{)}^{-2}}$ is