[tex]a)\ \ 2\cdot2^3\cdot8^5=2\cdot2^3\cdot(2^3)^5=2\cdot2^3\cdot2^{15}=2^{1+3+15}=2^{19}\\\\\\b)\ \ \frac{10^6}{5^6}:2^3=(\frac{10}{5})^6:2^3=2^6:2^3=2^{6-3}=2^3\\\\\\c)\ \ (4^5)^7=4^{35}=(2^2)^{35}=2^{70}\\\\\\d)\ \ \frac{1}{8}\cdot4^5=(\frac{1}{2})^3\cdot(2^2)^5=2^{-3}\cdot2^1^0=2^{-3+10}=2^7\\\\\\Zastosowano\ \ wzory\\\\a^m\cdot a^n=a^{m+n}\\\\a^m:a^n=a^{m-n}\\\\(a^m)^n=a^{m\cdot n}\\\\(\frac{1}{a})^n=a^{-n}[/tex]
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[tex]a)\ \ 2\cdot2^3\cdot8^5=2\cdot2^3\cdot(2^3)^5=2\cdot2^3\cdot2^{15}=2^{1+3+15}=2^{19}\\\\\\b)\ \ \frac{10^6}{5^6}:2^3=(\frac{10}{5})^6:2^3=2^6:2^3=2^{6-3}=2^3\\\\\\c)\ \ (4^5)^7=4^{35}=(2^2)^{35}=2^{70}\\\\\\d)\ \ \frac{1}{8}\cdot4^5=(\frac{1}{2})^3\cdot(2^2)^5=2^{-3}\cdot2^1^0=2^{-3+10}=2^7\\\\\\Zastosowano\ \ wzory\\\\a^m\cdot a^n=a^{m+n}\\\\a^m:a^n=a^{m-n}\\\\(a^m)^n=a^{m\cdot n}\\\\(\frac{1}{a})^n=a^{-n}[/tex]