Obliczenia
[tex](2\frac{1}{2})^{100}\cdot(\frac{4}{25})^{52}=(\frac{5}{2})^{100}\cdot((\frac{2}{5})^2)^{52}=(\frac{5}{2})^{100}\cdot((\frac{5}{2})^{-2})^{52}=\\\\=(\frac{5}{2})^{100}\cdot(\frac{5}{2})^{-2\cdot52}=(\frac{5}{2})^{100}\cdot(\frac{5}{2})^{-104}=(\frac{5}{2})^{100+(-104)}=\\\\=(\frac{5}{2})^{100-104}=(\frac{5}{2})^{-4}=(\frac{2}{5})^4=\frac{2^4}{5^4}=\frac{2\cdot2\cdot2\cdot2}{5\cdot5\cdot5\cdot5}=\frac{16}{625}[/tex]
Wykorzystane wzory działań na potęgach
[tex]a^{-n}=(\frac{1}{a})^n\\\\a^m\cdot a^n=a^{m+n}[/tex]