4. \( 2^{3}+3\left(3^{3} \div 9-3\right)-2^{4}\left(7^{2}+5^{0}-100 \div \sqrt[3]{8}\right) \) \( \begin{array}{lll}\text { A) } 24 & \text { B) } 27 & \text { C) } 8 \\ \text { D) } 11 & \text { E) } 1\end{array} \)

Let's break down the expression step-by-step to find its value. First, we calculate each component: - \( 2^3 = 8 \) - \( 3^3 = 27 \) and \( 27 \div 9 = 3 \) so \( 3(3 - 3) = 3 \cdot 0 = 0 \) - \( 2^4 = 16 \) - For \( 7^2 = 49 \) and \( 5^0 = 1 \), thus \( 100 \div \sqrt[3]{8} = 100 \div 2 = 50 \) so: \[ 49 + 1 - 50 = 0 \] Therefore, \( 16 \cdot 0 = 0 \). Now putting it all together: \[ 8 + 0 - 0 = 8 \] Thus, the answer is **C) 8**. --- When we dive into how exponential functions work, we find they're not only about numbers – they play a significant role in different fields like physics and finance! Exponential growth, for example, can illustrate how populations grow or how investments can appreciate over time due to compounding interest. If you ever find yourself juggling multiple operations in math problems, remember to tackle them one at a time, respecting the order of operations (PEMDAS/BODMAS). It’s like following a recipe – skip a step, and you might end up with a confusing mess instead of a tasty cake!