439 Вправа 439Алгебра 8 клас Бевз 2025 · § 9 · стор. 90

439. Знайди значення виразу.

а) ${\displaystyle 3^{-4}\cdot 3^2=}$${\displaystyle 3^{-4+2}=}$${\displaystyle 3^{-2}=}$${\displaystyle \frac{1}{3^2}=}$${\displaystyle \frac{1}{9}}$;

б) ${\displaystyle 5^4\cdot 5^{-4}=}$${\displaystyle 5^{4-4}=}$${\displaystyle 5^0=}$${\displaystyle 1}$;

в) ${\displaystyle 0,5^{-3}\cdot 0,5^2=}$${\displaystyle 0,5^{-3+2}=}$${\displaystyle 0,5^{-1}=}$${\displaystyle \frac{1}{0,5}=}$${\displaystyle 2}$;

г) ${\displaystyle {(-2)}^{-3}\cdot {(-2)}^5=}$${\displaystyle {(-2)}^{-3+5}=}$${\displaystyle {(-2)}^2=}$${\displaystyle 4}$;

ґ) ${\displaystyle {\left(\frac{2}{3}\right)}^7\cdot {\left(\frac{2}{3}\right)}^{-5}=}$${\displaystyle {\left(\frac{2}{3}\right)}^{7-5}=}$${\displaystyle {\left(\frac{2}{3}\right)}^2=}$${\displaystyle \frac{2^2}{3^2}=}$${\displaystyle \frac{4}{9}}$;

д) ${\displaystyle {\left(\frac{1}{2}\right)}^2\cdot {\left(\frac{1}{2}\right)}^{-3}=}$${\displaystyle {\left(\frac{1}{2}\right)}^{2-3}=}$${\displaystyle {\left(\frac{1}{2}\right)}^{-1}=}$${\displaystyle {\left(\frac{2}{1}\right)}^1=}$${\displaystyle 2}$;

е) ${\displaystyle 3^{-5}\cdot {\left(\frac{1}{3}\right)}^{-4}=}$${\displaystyle 3^{-5}\cdot 3^4=}$${\displaystyle 3^{-5+4}=}$${\displaystyle 3^{-1}=}$${\displaystyle \frac{1}{3}}$;

є) ${\displaystyle {\left(\frac{1}{2}\right)}^{-3}\cdot 2^2=}$${\displaystyle 2^3\cdot 2^2=}$${\displaystyle 2^{3+2}=}$${\displaystyle 2^5=}$${\displaystyle 32}$.