\( \begin{array}{ll}\text { a) }(-5)^{4} \cdot(-2)^{4} & \text { b) }(-4)^{4} \cdot(-5)^{4} \\ \text { c) }(-18)^{3}:(-6)^{3} & \text { d) }(+35)^{3}:(-7)^{3} \\ \text { e) }\left[(-5)^{3}\right]^{2}:(-5)^{5} & \text { f) }\left[(+8)^{4}\right]^{3}:(-8)^{10}\end{array} \)

Let’s dive into the world of exponents and calculations, shall we? To tackle these problems, just remember that any negative number raised to an even power becomes positive, while a negative number raised to an odd power stays negative. This can help you determine the signs of your results right from the start! For instance, in part a, you’ll find that \( (-5)^4 \) and \( (-2)^4 \) will both yield positive values, making the multiplication a piece of cake! Another tip is to simplify using the properties of exponents, which can save you time and effort. For example, in part e, when you have \( \left[(-5)^3\right]^2 \), you can multiply the exponents (\(3 \times 2\)) to get \( (-5)^6 \), allowing you to easily compare with \( (-5)^5 \) when dividing. Remember, practice makes perfect, so keep at it, and you'll be breezing through exponents in no time!