[tex]a)\ \ 3^9\cdot3^{-6}=3^{9+(-6)}=3^{9-6}=3^3=27\\\\b)\ \ 0,5^3\cdot0,5^7=0,5^{3+7}=0,5^{10}=(\frac{5}{10})^{10}=(\frac{1}{2})^{10}=\frac{1}{1024}\\\\c)\ \ (2^5)^{-2}=2^{5\cdot(-2)}=2^{-10}=(\frac{1}{2})^{10}=\frac{1}{1024}\\\\d)\ \ (0,25^{-1})^{-4}=0,25^{-1\cdot(-4)}=0,25^4=(\frac{25}{100})^4=(\frac{1}{4})^4=\frac{1}{256}\\\\e)\ \ 5^{-9}:5^{-11}=5^{-9-(-11)}=5^{-9+11}=5^2=25\\\\f)\ \ 4:4^{-4}=4^1:4^{-4}=4^{1-(-4)}=4^{1+4}=4^5=1024[/tex]
[tex]g)\ \ 6^5:3^5=(6:3)^5=2^5=32\\\\h)\ \ 10^{10}:5^{10}=(10:5)^{10}=2^{10}=1024\\\\i)\ \ 6^3\cdot2^{-5}=216\cdot(\frac{1}{2})^5=\not216^2^7\cdot\frac{1}{\not32_{4}}=\frac{27}{4}=6\frac{3}{4}\\\\j)\ \ 10^4\cdot5^{-2}=10000\cdot(\frac{1}{5})^2=\not10000^4^0^0\cdot\frac{1}{\not25_{1}}=400[/tex]
Wykorzystano własności potęg
[tex]a^m\cdot a^n=a^{m+n}\\\\a^m:a^n=a^{m-n}\\\\(a^m)^n=a^{m\cdot n}\\\\a^n\cdot b^n=(a\cdot b)^n\\\\a^n:b^n=(a:b)^n[/tex]
