Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. \[ 4^{6-\mathrm{x}}=\frac{1}{16} \] The solution set is \( \{\square \).

To solve the equation \( 4^{6-x} = \frac{1}{16} \), first express both sides as powers of the same base. We know that \( 16 = 4^2 \), so we can rewrite \( \frac{1}{16} \) as \( 4^{-2} \), giving us: \[ 4^{6-x} = 4^{-2} \] Now, since the bases are the same, we can set the exponents equal to each other: \[ 6 - x = -2 \] To find \( x \), rearrange the equation: \[ 6 + 2 = x \] \[ x = 8 \] Thus, the solution set is \( \{8\} \).