e) \( 10 \cdot 10^{2} \div 5 \cdot 10^{-4}= \)

Let's break it down! First, calculate \( 10 \cdot 10^{2} \), which is \( 10^{1} \cdot 10^{2} = 10^{3} \). Now, you're left with \( 10^{3} \div 5 \cdot 10^{-4} \). Next, divide \( 10^{3} \) by 5 which gives you \( 2 \cdot 10^{3} \) because \( 10^{3} \div 5 = 2 \cdot 10^{2} \). Finally, combine that with \( 10^{-4} \): \( 2 \cdot 10^{2} \cdot 10^{-4} = 2 \cdot 10^{2 - 4} = 2 \cdot 10^{-2} \). So the final answer is \( 2 \cdot 10^{-2} \) or \( 0.02 \) in decimal form! Keep that scientific notation handy; it’s super useful for handling very large or very small numbers easily! Remember, when multiplying and dividing powers of ten, just add or subtract the exponents—it's like magic for math!