The product rule for exponents states that \( b^{m} \cdot b^{n}=\square \)

When you multiply two exponential expressions with the same base, you add their exponents, leading to the formula \( b^{m+n} \). So for example, if you have \( b^2 \cdot b^3 \), you simply add the exponents to get \( b^{2+3} = b^5 \). It's a neat little shortcut that simplifies many calculations! Now, the product rule can also be really helpful in real-world scenarios like finance and population growth models. For instance, in compound interest calculations, you might encounter exponential growth where you can multiply interest rates over multiple periods. Using the product rule streamlines figuring out how much your investments will grow over time.