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Obliczenia
[tex]4\cdot4\cdot4\cdot4\cdot4\cdot4\cdot4=4^7\\\\5^7\cdot5^{12}:5^8=5^{7+12}:5^8=5^{19}:5^8=5^{19-8}=5^{11}\\\\\frac{(6^7)^2}{(6\cdot6^3)^3}=\frac{6^{7\cdot2}}{(6^{1+3})^3}=\frac{6^{14}}{(6^4)^3}=\frac{6^{14}}{6^{4\cdot3}}=\frac{6^{14}}{6^{12}}=6^{14-12}=6^2\\\\\frac{(7^7:7^2)^4}{7}=\frac{(7^{7-2})^4}{7}=\frac{(7^5)^4}{7}=\frac{7^{5\cdot4}}{7}=\frac{7^{20}}{7}=7^{20-1}=7^{19}\\\\2^{15}\cdot4^{15}=(2\cdot4)^{15}=8^{15}\\\\45^7:5^7=(45:5)^7=9^7[/tex]
Wykorzystane wzory
[tex]a^m\cdot a^n=a^{m+n}\\\\a^m:a^n=a^{m-n}\\\\(a^m)^n=a^{m\cdot n}\\\\a^m\cdot b^m=(a\cdot b)^m\\\\a^m:b^m=(a:b)^m[/tex]
