Tính: a) (1/5)^-2

Bài 6.1 trang 9 Toán 11 Tập 2: Tính:

a) ${\left(\frac{1}{5}\right)}^{-2}$;

b) $4^{\frac{3}{2}}$;

c) ${\left(\frac{1}{8}\right)}^{-\frac{2}{3}}$;

d) ${\left(\frac{1}{16}\right)}^{-0,75}$.

Trả lời

a) ${\left(\frac{1}{5}\right)}^{-2}=5^2=25$.

b) $4^{\frac{3}{2}}=\sqrt{4^3}=\sqrt{64}=8$.

c) ${\left(\frac{1}{8}\right)}^{-\frac{2}{3}}=8^{\frac{2}{3}}=\sqrt[3]{8^2}=\sqrt[3]{{\left(2^3\right)}^2}=\sqrt[3]{{\left(2^2\right)}^3}=2^2=4$.

d) ${\left(\frac{1}{16}\right)}^{-0,75}={16}^{0,75}={16}^{\frac{3}{4}}=\sqrt[4]{{16}^3}=\sqrt[4]{{\left(2^4\right)}^3}=\sqrt[4]{{\left(2^3\right)}^4}=2^3=8$.