463 Вправа 463Алгебра 8 клас Бевз 2025 · § 9 · стор. 93

463. Спрости вираз (n — ціле число).

а) ${\displaystyle \frac{x^{6n}{y}^{n+4}}{x^{2n}{y}^{n+5}}=}$${\displaystyle x^{6n-2n}{y}^{n+4-n-5}=}$${\displaystyle x^{4n}{y}^{-1}}$;

б) ${\displaystyle \frac{a^{3n}{b}^{n-3}}{a^{2n}{b}^{n-5}}=}$${\displaystyle a^{3n-2n}{b}^{n-3-n+5}=}$${\displaystyle a^n{b}^2}$;

в) ${\displaystyle \frac{x^{-2n}+x^n}{x^{-n}}=}$${\displaystyle \frac{x^{-2n}}{x^{-n}}+\frac{x^n}{x^{-n}}}$=

=${\displaystyle x^{-2n+n}+x^{n+n}=}$${\displaystyle x^{-n}+x^{2n}}$;

г) ${\displaystyle \frac{a^{2n}-a^{-3n}}{a^{-2n}}=}$${\displaystyle \frac{a^{2n}}{a^{-2n}}-\frac{a^{-3n}}{a^{-2n}}}$=

=${\displaystyle a^{2n+2n}-a^{-3n+2n}=}$${\displaystyle a^{4n}-a^{-n}}$.