$$ {({1\over25})^{-1\over2}}+{({8\over 27})^{-1\over3}}$$

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

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. $$ ^{4}{\sqrt{9}}>{^{3}{\sqrt{15}}}>{^{6}{\sqrt{24}}}$$

If $$  3 ^{2x-y}=3^{x+y}=\sqrt{27}$$ then the value of y is

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

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

If $$ {2^{2n-1}}={1\over8^{n-3}}$$,then the value of n is:

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