Odpowiedź:
[tex]a)\\\\(2^{10}\cdot2^5\cdot7^4)^2=2^{m}\cdot7^{n}\\\\(2^1^0\cdot2^5\cdot7^4)^2=(2^1^5\cdot7^4)^2=(2^1^5)^2\cdot(7^4)^2=2^{30}\cdot7^8\\\\m=30\ \ ,\ \ n=8\\\\\\b)\\\\\frac{(3^4\cdot5^7)^3}{5^9}=3^m\cdot5^n\\\\\\\dfrac{(3^4\cdot5^7)^3}{5^9}=\dfrac{(3^4)^3\cdot(5^7)^3}{5^9}=\dfrac{3^1^2\cdot5^2^1}{5^9}=3^{12}\cdot\dfrac{5^2^1}{5^9}=3^{12}\cdot5^{21-9}=3^1^2\cdot5^{12}\\\\\\m=12\ \ ,\ \ n=12[/tex]
[tex]c)\\\\4\cdot(\frac{2^3}{3^4})^1^0=\frac{2^{m}}{3^{n}}\\\\\\4\cdot\left(\dfrac{2^3}{3^4}\right)^{10}=2^2\cdot\dfrac{(2^3)^{10}}{(3^4)^1^0}=2^2\cdot\dfrac{2^{30}}{3^{40}}=\dfrac{2^2\cdot2^3^0}{3^4^0}=\dfrac{2^{2+30}}{3^4^0}=\dfrac{2^3^2}{3^4^0}\\\\\\m=32\ \ ,\ \ n=40[/tex]
[tex]d)\\\\(\frac{7^3}{5^2})^3\cdot(\frac{5^3}{7^5})^4=\frac{5^{m}}{7^{n}}\\\\\\\left(\dfrac{7^3}{5^2}\right)^3\cdot\left(\dfrac{5^3}{7^5}\right)^4=\dfrac{(7^3)^3}{(5^2)^3}\cdot\dfrac{(5^3)^4}{(7^5)^4}=\dfrac{7^9}{5^6}\cdot\dfrac{5^1^2}{7^2^0}=\dfrac{5^{12-6}}{7^{20-9}}=\dfrac{5^6}{7^1^1}\\\\\\m=6\ \ ,\ \ n=11[/tex]
