Ответ:
Применяем свойства степеней : [tex]\bf \Big(\dfrac{a}{b}\Big)^{n}=\dfrac{a^{n}}{b^{n}}\ \ ,\ \ \ (a^{k})^{n}=a^{k+n}[/tex] .
[tex]\bf \displaystyle \Big(\frac{a^3}{c^2}\Big)^4=\frac{(a^3)^4}{(c^2)^4}=\frac{a^{12}}{c^8}\ \ ,\ \ \ \ \Big(\frac{2a^3}{3\, b^4}\Big)^5=\frac{(2a^3)^5}{(3\, b^4)^5}=\frac{32\, a^{15}}{243\, b^{20}}\ \ ,\\\\\\\Big(\frac{3x^2y^4}{4m^3}\Big)^2=\frac{(3x^2y^4)^2}{(4m^3)^2}=\frac{9\, x^4y^{8}}{16\, m^6}\\\\\\\Big(-\frac{10m^2}{3\, n^2\, p^3}\Big)^3=-\frac{(10\, m^2)^3}{(3\, n^2\, p^3)^3}=-\frac{1000\, m^{6}}{27\,n^6\, p^9}[/tex]
[tex]\bf \Big(-\dfrac{5\, a^3}{3\, b^2\, c^4}\Big)^4=\dfrac{(5\, a^3)^4}{(3\, b^2\, c^4)^4}=\dfrac{625\, a^{12}}{81\, b^8\, c^{16}}\\\\\\\Big(-\dfrac{b^3\, c^2}{8\, a^3}\Big)^2=\dfrac{(b^3\, c^2)^2}{(8\, a^3)^2}=\dfrac{b^6\, c^{4}}{64\, a^6}[/tex]
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Ответ:
Применяем свойства степеней : [tex]\bf \Big(\dfrac{a}{b}\Big)^{n}=\dfrac{a^{n}}{b^{n}}\ \ ,\ \ \ (a^{k})^{n}=a^{k+n}[/tex] .
[tex]\bf \displaystyle \Big(\frac{a^3}{c^2}\Big)^4=\frac{(a^3)^4}{(c^2)^4}=\frac{a^{12}}{c^8}\ \ ,\ \ \ \ \Big(\frac{2a^3}{3\, b^4}\Big)^5=\frac{(2a^3)^5}{(3\, b^4)^5}=\frac{32\, a^{15}}{243\, b^{20}}\ \ ,\\\\\\\Big(\frac{3x^2y^4}{4m^3}\Big)^2=\frac{(3x^2y^4)^2}{(4m^3)^2}=\frac{9\, x^4y^{8}}{16\, m^6}\\\\\\\Big(-\frac{10m^2}{3\, n^2\, p^3}\Big)^3=-\frac{(10\, m^2)^3}{(3\, n^2\, p^3)^3}=-\frac{1000\, m^{6}}{27\,n^6\, p^9}[/tex]
[tex]\bf \Big(-\dfrac{5\, a^3}{3\, b^2\, c^4}\Big)^4=\dfrac{(5\, a^3)^4}{(3\, b^2\, c^4)^4}=\dfrac{625\, a^{12}}{81\, b^8\, c^{16}}\\\\\\\Big(-\dfrac{b^3\, c^2}{8\, a^3}\Big)^2=\dfrac{(b^3\, c^2)^2}{(8\, a^3)^2}=\dfrac{b^6\, c^{4}}{64\, a^6}[/tex]