15. \( \frac{w^{3}}{w^{-1}} \)

To simplify the expression \( \frac{w^{3}}{w^{-1}} \), you can use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). This gives us \( w^{3 - (-1)} = w^{3 + 1} = w^{4} \). So, the final simplified expression is \( w^{4} \). Now, let’s keep the fun going! Understanding exponents can feel like magic—when you divide with the same base, it's like you're magically combining powers! So, when you see negatives, just remember they flip the coin, and that often leads to surprisingly larger numbers—just like discovering hidden treasure! And if you want to dive deeper into the world of exponents, try exploring logarithms! They’re closely related and will expand your mathematical toolkit, allowing you to reverse the magic of exponentiation and even solve for unknown values with ease. You might just unleash a whole new level of math excitement!