Potęgi
: 7 paź 2008, o 22:03
\(\displaystyle{ \frac{(8^{n-2}+8^{n-3})^{3}}{(4^{n-1}-4^{n-2})^{3}}}\)
\(\displaystyle{ \frac{(8^{n-2}+8^{n-3})^{3}}{(4^{n-1}-4^{n-2})^{3}} =
ft( \frac{8^{n-3}(8+1)}{4^{n-2}(4-1)} \right)^3 =
ft( \frac{9 2^{n-3} 4^{n-3}}{3 4 4^{n-3}} \right)^3 =\\=
ft( \frac{3 2^{n-3}}{2^2} \right)^3 = (3 2^{n-5})^3 = 27 2^{3n-15} = 27 8^{n-5}}\)