350 Вправа 350Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 97

350. Запишіть як степінь:

1) ${\displaystyle {\left(a^{-8}\right)}^n:{\left(a^n\right)}^{-1}=}$${\displaystyle a^{-8n}:a^{-n}=}$${\displaystyle a^{-8n+n}=}$${\displaystyle a^{-7n}}$;

2) ${\displaystyle {\left(a^m\right)}^{-n}\cdot {\left(a^n\right)}^p=}$${\displaystyle a^{-mn}\cdot a^{np}=}$${\displaystyle a^{np-mn}}$;

3) ${\displaystyle {(a^{-15}:a^4)}^{-3}\cdot {(a^{10}:a^3)}^{-2}=}$${\displaystyle {\left(a^{-19}\right)}^{-3}\cdot {\left(a^7\right)}^{-2}=}$${\displaystyle a^{57}\cdot a^{-14}=}$${\displaystyle a^{43}}$;

4) ${\displaystyle {\left(a^{-15}{a}^4\right)}^3:{\left(a^{10}{a}^{-3}\right)}^{-2}=}$${\displaystyle {\left(a^{-11}\right)}^3:{\left(a^7\right)}^{-2}=}$${\displaystyle a^{-33}:a^{-14}=}$${\displaystyle a^{-33+14}=}$${\displaystyle a^{-19}}$;

5) ${\displaystyle {\left(a^{-15}{a}^{-4}\right)}^3:{\left(a^{10}{a}^3\right)}^{-2}=}$${\displaystyle {\left(a^{-19}\right)}^3:{\left(a^{13}\right)}^{-2}=}$${\displaystyle a^{-57}:a^{-26}=}$${\displaystyle a^{-57+26}=}$${\displaystyle a^{-31}}$;

6) ${\displaystyle {\left(a^{15}{a}^{-4}\right)}^3\cdot {\left(a^{-10}{a}^3\right)}^2=}$${\displaystyle {\left(a^{11}\right)}^3\cdot {\left(a^{-7}\right)}^2=}$${\displaystyle a^{33}\cdot a^{-14}=}$${\displaystyle a^{19}}$;

7) ${\displaystyle {(-a)}^{-2n}=}$${\displaystyle a^{-2n}}$ (парний показник):

${\displaystyle a^{2n-n^2}\cdot a^{n-n^2}:a^{-2n}=}$${\displaystyle a^{2n-n^2+n-n^2+2n}=}$${\displaystyle a^{5n-2n^2}}$;

8) ${\displaystyle (2+n)(2-n)=}$${\displaystyle 4-n^2}$:

${\displaystyle a^{-n^2}\cdot a^{-(4-n^2)}:a^{-4}=}$${\displaystyle a^{-n^2-4+n^2+4}=}$${\displaystyle a^0=}$${\displaystyle 1}$.