190° Вправа 190Алгебра 8 клас Тарасенкова 2025 · § 5 · стор. 57

190. Піднесіть до степеня.

Підносимо до степеня і чисельник, і знаменник: ${\displaystyle {\left(\frac{A}{B}\right)}^n=}$${\displaystyle \frac{A^n}{B^n}}$; ${\displaystyle {\left(a^m\right)}^n=}$${\displaystyle a^{mn}}$. Від’ємний дріб у парному степені — додатний, у непарному — від’ємний.

1) ${\displaystyle {\left(\frac{x^2}{6}\right)}^2=}$${\displaystyle \frac{{\left(x^2\right)}^2}{6^2}=}$${\displaystyle \frac{x^4}{36}}$;

2) ${\displaystyle {\left(\frac{3}{y}\right)}^3=}$${\displaystyle \frac{3^3}{y^3}=}$${\displaystyle \frac{27}{y^3}}$;

3) ${\displaystyle {\left(\frac{x}{2y}\right)}^2=}$${\displaystyle \frac{x^2}{2^2{y}^2}=}$${\displaystyle \frac{x^2}{4y^2}}$;

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

5) ${\displaystyle {\left(\frac{2a^2}{3}\right)}^3=}$${\displaystyle \frac{2^3{\left(a^2\right)}^3}{3^3}=}$${\displaystyle \frac{8a^6}{27}}$;

6) ${\displaystyle {\left(\frac{3a^2}{4b^4}\right)}^3=}$${\displaystyle \frac{3^3{\left(a^2\right)}^3}{4^3{\left(b^4\right)}^3}=}$${\displaystyle \frac{27a^6}{64b^{12}}}$;

7) ${\displaystyle {(-\frac{x^3}{8y^5})}^2=}$${\displaystyle \frac{{\left(x^3\right)}^2}{8^2{\left(y^5\right)}^2}=}$${\displaystyle \frac{x^6}{64y^{10}}}$;

8) ${\displaystyle {(-\frac{a^5}{6b^4})}^3=}$${\displaystyle -\frac{{\left(a^5\right)}^3}{6^3{\left(b^4\right)}^3}=}$${\displaystyle -\frac{a^{15}}{216b^{12}}}$.