205 Вправа 205Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 59

205. Спростіть вираз:

1) Підносимо до степенів:

${\displaystyle {\left(\frac{2x^2{y}^3}{a^3{b}^5}\right)}^2=}$${\displaystyle \frac{4x^4{y}^6}{a^6{b}^{10}}}$; ${\displaystyle {\left(\frac{3a^{2}b}{4x{y}^2}\right)}^3=}$${\displaystyle \frac{27a^6{b}^3}{64x^3{y}^6}}$;

${\displaystyle \frac{4x^4{y}^6}{a^6{b}^{10}}\cdot \frac{27a^6{b}^3}{64x^3{y}^6}\cdot \frac{16b^2}{9x}=}$${\displaystyle \frac{4\cdot 27\cdot 16\cdot a^6{b}^5{x}^4{y}^6}{64\cdot 9\cdot a^6{b}^{10}{x}^4{y}^6}=}$${\displaystyle \frac{1728\cancel{a^6{b}^5{x}^4{y}^6}}{576\cancel{a^6{b}^5{x}^4{y}^6}{b}^5}=}$${\displaystyle \frac{3}{b^5}}$;

2) Дія в дужках:

${\displaystyle {\left(\frac{5abc}{3xyz}\right)}^3\cdot \frac{9xy{z}^2}{25a{c}^2}=}$${\displaystyle \frac{125a^3{b}^3{c}^3}{27x^3{y}^3{z}^3}\cdot \frac{9xy{z}^2}{25a{c}^2}=}$${\displaystyle \frac{\stackrel{1}{\cancel{125}}\cdot \stackrel{1}{\cancel{9}}{a}^3{b}^3{c}^{3}xy{z}^2}{\underset{1}{\cancel{27}}\cdot \underset{1}{\cancel{25}}\cdot a{c}^2{x}^3{y}^3{z}^3}=}$${\displaystyle \frac{5a^2{b}^{3}c}{3x^2{y}^{2}z}}$;

${\displaystyle {\left(\frac{5a^2{b}^{3}c}{3x^2{y}^{2}z}\right)}^2=}$${\displaystyle \frac{25a^4{b}^6{c}^2}{9x^4{y}^4{z}^2}}$.