№ 4. Сократите дроби: а) 5b²/(6b); б) 9a⁴/(10a³); в) −5a⁴/(10a⁵); г) 3y⁴/y³; д) 21z⁸/(3yz); е) 12x³/(-42x³).

Используем правило $\backslash (\backslash frac\{x^m\}\{x^n\}\backslash )=x^\{m-n\}$ и сокращаем общие множители.

1. а) $\backslash (\backslash frac\{5b^2\}\{6b\}\backslash )=\backslash (\backslash frac\{5b\}\{6\}\backslash )$.
2. б) $\backslash (\backslash frac\{9a^4\}\{10a^3\}\backslash )=\backslash (\backslash frac\{9a\}\{10\}\backslash )$.
3. в) $\backslash (\backslash frac\{-5a^4\}\{10a^5\}\backslash )=-\backslash (\backslash frac\{1\}\{2a\}\backslash )$.
4. г) $\backslash (\backslash frac\{3y^4\}\{y^3\}\backslash )=3y$.
5. д) $\backslash (\backslash frac\{21z^8\}\{3yz\}\backslash )=\backslash (\backslash frac\{7z^7\}\{y\}\backslash )$.
6. е) $\backslash (\backslash frac\{12x^3\}\{-42x^3\}\backslash )=-\backslash (\backslash frac\{2\}\{7\}\backslash )$.

Ответ: а) 5b/6; б) 9a/10; в) −1/(2a); г) 3y; д) 7z⁷/y; е) −2/7.