If $$ {3^{4x-y}={3^{x+y}=\sqrt{27}}}$$,  then the value of y is:

If $$ {81\ × 343\ ×625}={3^{p}}\ {7^{q}}\ {5^{r}}$$ then find out the value of  $$ {\sqrt{(p-r)^{2}+q^{2}}}$$.

Find out the value of $$ {\sqrt{(121)}} +{\sqrt{(12321)}}+{\sqrt{(1234321)}}$$.

Find the cube root of $$ ^{3}\sqrt{-13824}$$.

$$ {{2^n+2^{n-1}}\over {2^{n+1} -2^n}}=?$$

If  $$ {x^{\sqrt{x}}}={({x{\sqrt{x}}})^{x}}$$, then the find the value of x

Which of the following statements is/are True?
I. $$ {\sqrt{12}}>{^{3}{\sqrt{16}}}>{^{4}{\sqrt{24}}}$$
II. $$ ^{3}{\sqrt{25}}>{^{4}{\sqrt{32}}}>{^{6}{\sqrt{48}}}$$
III. $$ ^{4}{\sqrt{9}}>{^{3}{\sqrt{15}}}>{^{6}{\sqrt{24}}}$$

Which of the following statements is /are True?
I. $$ {33^3}>{3^{33}}$$
II. $$ {333}>{(3^{3})^{3}}$$