If$3^{(x-y)}=27$  and$3^{(x+y)}=243$, then $x$ is equal to

What is the simplified value of $\left[\left(\sqrt{9}+\sqrt{7}\right)÷\left(\sqrt{9}-\sqrt{7}\right)\right]$?

What is the simplified value of $\left[\left(\sqrt{41}+\sqrt{7}\right) ÷\left(\sqrt{41}-\sqrt{7}\right)\right]?$

Which of the following statement is true?

I. $\sqrt[9]{6}>\sqrt[18]{5}$

II. $\sqrt[4]{7}>\sqrt[6]{11}$ 

What is the largest value of $n$ such that ${10}^n$ divides the product? 

$2^5\times 3^3\times 4^8\times 5^3\times 6^7\times 7^6\times 8^{12}\times 9^9\times {10}^6\times {15}^{12}\times {20}^{14}\times {22}^{11}\times {25}^{15}=?$

Which of the following relation(s) is/are true? 

$$\begin{gathered} I. \sqrt{2}>\sqrt[3]{3} \\ II. \sqrt[3]{3}>\sqrt{2} \\ III. \sqrt{2}=\sqrt[3]{3} \end{gathered}$$

$1$. $\sqrt{676}+\sqrt{6.76}+\sqrt{0.0676}=27.76$

$2$. $\sqrt{339+\sqrt{36}+\sqrt{49}+\sqrt{81}}=19$