[tex]a)\ \ (6\cdot11^3)^5=6^5\cdot(11^3)^5=6^5\cdot11^{15}\ \ \ \ \to\ \ m=5\ ,n=15\\\\\\b)\ \ \left(\dfrac{3^4}{5}\right)^7=\dfrac{(3^4)^7}{5^7}=\dfrac{3^2^8}{5^7}\ \ \ \ \to\ \ m=28\ ,n=7\\\\\\c)\ \ (2^3\cdot5^9)^2=(2^3)^2\cdot(5^9)^2=2^6\cdot5^{18}\ \ \ \ \to\ \ m=6\ ,n=18\\\\\\d)\ \ (7^{10}\cdot3^5)^6=(7^1^0)^6\cdot(3^5)^6=7^{60}\cdot3^{30}\ \ \ \ \to\ \ m=60\ , n=30[/tex]
[tex]e)\ \ \left(\dfrac{10^4}{11^7}\right)^5=\dfrac{(10^4)^5}{(11^7)^5}=\dfrac{10^2^0}{11^3^5}\ \ \ \ \to\ \ m=20\ , n=35\\\\\\f)\ \ \left(\dfrac{6^1^2}{13^5}\right)^3=\dfrac{(6^1^2)^3}{(13^5)^3}=\dfrac{6^3^6}{13^1^5}\ \ \ \ \to\ \ m=36\ ,n=15[/tex]
[tex]Zastosowano\ \ wzory\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(a^m)^n=a^{m\cdot n}\\\\(\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]
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[tex]a)\ \ (6\cdot11^3)^5=6^5\cdot(11^3)^5=6^5\cdot11^{15}\ \ \ \ \to\ \ m=5\ ,n=15\\\\\\b)\ \ \left(\dfrac{3^4}{5}\right)^7=\dfrac{(3^4)^7}{5^7}=\dfrac{3^2^8}{5^7}\ \ \ \ \to\ \ m=28\ ,n=7\\\\\\c)\ \ (2^3\cdot5^9)^2=(2^3)^2\cdot(5^9)^2=2^6\cdot5^{18}\ \ \ \ \to\ \ m=6\ ,n=18\\\\\\d)\ \ (7^{10}\cdot3^5)^6=(7^1^0)^6\cdot(3^5)^6=7^{60}\cdot3^{30}\ \ \ \ \to\ \ m=60\ , n=30[/tex]
[tex]e)\ \ \left(\dfrac{10^4}{11^7}\right)^5=\dfrac{(10^4)^5}{(11^7)^5}=\dfrac{10^2^0}{11^3^5}\ \ \ \ \to\ \ m=20\ , n=35\\\\\\f)\ \ \left(\dfrac{6^1^2}{13^5}\right)^3=\dfrac{(6^1^2)^3}{(13^5)^3}=\dfrac{6^3^6}{13^1^5}\ \ \ \ \to\ \ m=36\ ,n=15[/tex]
[tex]Zastosowano\ \ wzory\\\\(a\cdot b)^n=a^n\cdot b^n\\\\(a^m)^n=a^{m\cdot n}\\\\(\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]