8) \( \frac{1^{0}+2^{-1}}{3^{-2}+4^{-1}} \)

Let's break this down step by step! First, we evaluate the terms in the numerator: - \( 1^{0} = 1 \) (any non-zero number raised to the power of 0 is 1) - \( 2^{-1} = \frac{1}{2} \) So, the numerator becomes: \[ 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \] Now for the denominator: - \( 3^{-2} = \frac{1}{3^{2}} = \frac{1}{9} \) - \( 4^{-1} = \frac{1}{4} \) Next, we find a common denominator for the denominator: \[ \frac{1}{9} + \frac{1}{4} = \frac{4}{36} + \frac{9}{36} = \frac{13}{36} \] Now, we put it all together: \[ \frac{\frac{3}{2}}{\frac{13}{36}} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{3}{2} \times \frac{36}{13} = \frac{108}{26} = \frac{54}{13} \] Thus, the final answer is: \[ \frac{54}{13} \]