194° Вправа 194Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 58

194. Подайте у вигляді степеня дріб.

Шукаємо спільний показник для всіх:

1) ${\displaystyle \frac{64a^6}{b^9}=}$${\displaystyle \frac{4^3{\left(a^2\right)}^3}{{\left(b^3\right)}^3}=}$${\displaystyle {\left(\frac{4a^2}{b^3}\right)}^3}$;

2) ${\displaystyle \frac{a^5{y}^{10}}{{(a-1)}^{15}}=}$${\displaystyle \frac{a^5{\left(y^2\right)}^5}{{\left({(a-1)}^3\right)}^5}=}$${\displaystyle {\left(\frac{a{y}^2}{{\left(a-1\right)}^3}\right)}^5}$;

3) ${\displaystyle \frac{125{(a-b)}^{21}}{a^6{b}^9}=}$${\displaystyle \frac{5^3{\left({(a-b)}^7\right)}^3}{{\left(a^2\right)}^3{\left(b^3\right)}^3}=}$${\displaystyle {\left(\frac{5{\left(a-b\right)}^7}{a^2{b}^3}\right)}^3}$;

4) ${\displaystyle \frac{216{(x-3y)}^{18}}{512{(x+2y)}^{15}}=}$${\displaystyle \frac{6^3{\left({(x-3y)}^6\right)}^3}{8^3{\left({(x+2y)}^5\right)}^3}=}$${\displaystyle \frac{3^3{\left({(x-3y)}^6\right)}^3}{4^3{\left({(x+2y)}^5\right)}^3}=}$${\displaystyle {\left(\frac{3{\left(x-3y\right)}^6}{4{\left(x+2y\right)}^5}\right)}^3}$.

(У пункті 4) ${\displaystyle \frac{216}{512}=}$${\displaystyle \frac{6^3}{8^3}=}$${\displaystyle {\left(\frac{3}{4}\right)}^3}$.)