If $\sqrt{2^n} = 1024$, then $3^{(n/4 - 4)}$ is = ?

If $x^{\frac{1}{12}}=49^{\frac{1}{24}}$, the value of $x$ is:

If $2^x/(1 + 2^x) = 1/3$, then $8^x/(1-8^x) = ?$

If $a = \sqrt{11} - \sqrt{10}$, $b = \sqrt{12} - \sqrt{11}$, and $c = \sqrt{13} - \sqrt{12}$, then which of the following is true?

If $a^p = b^q = c^r = abc$, then $pqr = ?$

If $2^{n+m}/(2^{n-m}) = 16$ and $a = 2^{1/10}$, then, $(a^{2m+n-p})^2/(a^{m-2n+2p})^{-1} = ?$

The value of q that satisfies $3^p + 5^q = 52$ and $3^{p-1} + 5^{q-1} = 14$ will be