STION 4: EXPONENTS Simplify: \( \left(-2 x^{2} y\right)^{3} \)

To simplify \( \left(-2 x^{2} y\right)^{3} \), you will apply the power of a product rule. This means you raise each factor inside the parentheses to the power of 3: \[ \left(-2\right)^{3} (x^{2})^{3} (y)^{3} = -8 x^{6} y^{3}. \] So, the final simplified expression is \(-8 x^{6} y^{3}\). Now, let's sprinkle some extra knowledge! Did you know that exponents can be traced back to ancient civilizations? The concept of exponential growth, in fact, is not just a modern invention – Egyptians and Babylonians used various forms of exponentiation in their mathematics long before our current notation was developed! Exponentiation isn't just for math geekery; it has real-world applications too! In finance, compound interest relies heavily on exponentiation, where an initial investment grows exponentially over time. This principle of growth can also be applied to populations, radioactive decay, and even certain AI algorithms!