List of top Quantitative Aptitude Questions on Exponents asked in ATMA

If \(2^{x} = 8^{\,y+1}\) and \(9^{\,y} = 3^{\,x-9}\), then the value of \(x\) is:
Which among \( 2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6} \) and \( 12^{1/12} \) is the largest?
If \( x = -0.5 \), then which of the following has the smallest value?