If \( \frac{\left(2^{2}\right)^{y}}{(2)^{24}}=1 \), then \( y= \)

To solve the equation \( \frac{\left(2^{2}\right)^{y}}{(2)^{24}}=1 \), we start by simplifying the left-hand side: \[ \left(2^{2}\right)^{y} = 2^{2y} \] So the equation becomes: \[ \frac{2^{2y}}{2^{24}} = 1 \] Using the properties of exponents, we can rewrite the left-hand side: \[ 2^{2y - 24} = 1 \] Since \( 2^0 = 1 \), we set the exponent equal to zero: \[ 2y - 24 = 0 \] Now, we can solve for \( y \): \[ 2y = 24 \] \[ y = \frac{24}{2} = 12 \] Thus, the solution is: \[ y = 12 \]