I stumbled upon the following in a textbook, and I can't understand what rules are used/how it converts it. Part of my problem is that im not quite sure what questions to ask, or how to formulate it.
$$(1,5)^{k-2}+(1,5)^{k-3} $$
Is converted into:
$$(1,5)^{k-1}*((1,5)^{-1}+(1,5)^{-2})$$
Would greatly appreciate it if anyone would take the time to point to the rules used or walk through it step by step. I have tried looking up rules for exponents and parenthesis but have not been able to find what I was looking for, also tried searching on stackexchange, but I think I might be failing to find the answer due to not searching for the right string.
Take the last expression you have, and distribute: i.e. do $a(b+c) = ab + ac$ with $a=(1.5)^{k-1}$, $b=(1.5)^{-1}$, and $(1.5)^{-2}$.
Then $$(1.5)^{k-1} \cdot (1.5)^{-1} = (1.5)^{(k-1) + (-1)} = (1.5)^{k-2}$$ and $$(1.5)^{k-1} \cdot (1.5)^{-2} = (1.5)^{(k-1) + (-2)} = (1.5)^{k-3}$$ and you arrive at the original expression. These last two steps are due to the rule $x^y \cdot x^z = x^{y+z}$.