y \( 2 k^{3} \) \( (2 k)^{-3} \) m) \( (-2 x)^{-3} \) i) \( 4 x^{-1} y-2 \) o) \( -5 x^{-3} y x^{-2} \) p) \( 2^{-2} x^{6} y^{-3} \)

Let’s dive into the world of exponents and see how these expressions play out! The expression \( y (2 k^{3}) \) simplifies to \( 2 k^{3} y \) and showcases that multiplying variables can be quite straightforward. Meanwhile, \( (2 k)^{-3} \) means you're dealing with \( \frac{1}{(2k)^{3}} = \frac{1}{8k^{3}} \). That’s just one of the ways negative exponents can flip things upside down! In practical scenarios, handling exponents can save you a ton of space and effort in calculations, especially in fields like physics and engineering where formulas rely heavily on powers. For example, when calculating gravitational force, you might come across distance raised to a power—knowing how to manipulate exponents could mean the difference between the right trajectory and a big ol’ miscalculation!