[tex]a) \ 2^{3^{3}} : (2^2)^{14} = 2^9 : 2^{28} = 2^{9 - 28} = 2^{-19} = \frac{1}{2^{19}} = \frac{1}{524228} \\\\ b) \ \frac{(2 \cdot 3^4)^4}{3^{18}} = \frac{2^4 \cdot 3^{16}}{3^{18}} = 2^4 \cdot \frac{3^{16}}{3^{18}} = 2^4 \cdot 3^{16 - 18} = 2^4 \cdot 3^{-2} = \frac{16}{9} \\\\
c) \ x^m \cdot x^n = x^{m + n} \\\\
d) \ x^m : x^n = x^{m - n} \\\\
e) \ (x^m)^n = x^{mn} \\\\
f) \ (x \cdot y)^m = x^m \cdot y^m[/tex]
