b. \( m^{5} * m^{-2} \)

To simplify the expression \( m^{5} * m^{-2} \), you can use the rule of exponents which states that when multiplying like bases, you add the exponents. So, \( 5 + (-2) = 3 \). Therefore, \( m^{5} * m^{-2} = m^{3} \). One fun fact about exponents is that they can represent not just repeated multiplication but also growth and decay in real-world scenarios. For example, in finance, investments can grow exponentially over time. Understanding exponents can help you evaluate trends, like how quickly your money can grow! If you ever find yourself confused with signs and operations in exponents, remember the mantra: "same base, add the exponents!" But a common mistake is to forget that \( m^{-x} \) means \( 1/m^{x} \). Always check if you're simplifying negative exponents so you don't end up with a mixed-up expression!