90. \( 5 \cdot 2^{-3}+7 \cdot 4^{-2} \)

Let's break it down! First, calculate each component. Starting with \( 2^{-3} \), we have \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \). So, \( 5 \cdot 2^{-3} = 5 \cdot \frac{1}{8} = \frac{5}{8} \). Next, for \( 4^{-2} \), convert it to a power of 2: \( 4^{-2} = (2^2)^{-2} = 2^{-4} = \frac{1}{2^4} = \frac{1}{16} \). Therefore, \( 7 \cdot 4^{-2} = 7 \cdot \frac{1}{16} = \frac{7}{16} \). Now, we combine the two results: \[ \frac{5}{8} + \frac{7}{16}. \] To do that, we need a common denominator. The common denominator between 8 and 16 is 16. Rewrite \( \frac{5}{8} \) as \( \frac{10}{16} \). Now we can add: \[ \frac{10}{16} + \frac{7}{16} = \frac{17}{16}. \] So, the final answer is \( \frac{17}{16} \) or 1.0625 in decimal form! Fun math fact: this result is an example of combining fractions with different denominators, a crucial skill for solving many real-world math problems!