The laws of exponents I will be using are:
[tex](x^y)^z = x^{yz}[/tex], and [tex]x^y \cdot x^z = x^{y+z}[/tex].
For the first part, [tex](15^3)^3 \cdot 15^{-6} = 15^9 \cdot 15^{-6} = 15^3[/tex].
For the second part, [tex]15 \cdot (15^3)^2 \cdot (15^{-5})^2 = 15 \cdot (15^6) \cdot (15^{-10}) = 15^{1+6-10} = 15^{-3} = \frac{1}{15^3}[/tex].
