253 Вправа 253Алгебра 8 клас Бевз 2025 · § 5 · стор. 53

253. Подай дріб у вигляді степеня.

а) ${\displaystyle \frac{a^{15}\cdot x^{30}}{{(a+x)}^{15}}=}$${\displaystyle \frac{a^{15}\cdot {\left(x^2\right)}^{15}}{{(a+x)}^{15}}=}$${\displaystyle {\left(\frac{a{x}^2}{a+x}\right)}^{15}}$;

б) ${\displaystyle \frac{{(x-y)}^{10}\cdot {(x+y)}^{20}}{{(2x+y)}^{20}}}$=

=${\displaystyle \frac{{(x-y)}^{10}\cdot {\left({(x+y)}^2\right)}^{10}}{{\left({(2x+y)}^2\right)}^{10}}=}$${\displaystyle {\left(\frac{\left(x-y\right){\left(x+y\right)}^2}{{\left(2x+y\right)}^2}\right)}^{10}}$.