71. Ifodalarni soddalashtiring: a) √(2⁻¹), √(2⁰), √2, √(2²), √(2³), √(2²⁰¹⁷); b) √(10⁻⁵), √(10⁻⁴), √(10⁻³), √(10⁻²), √(10⁻¹).

Darajali ildizdan foydalanamiz: \(\sqrt{a^n}=a^{n/2}\).

a)

\(\sqrt{2^{-1}}=2^{-1/2}=\frac{\sqrt2}{2}\);
\(\sqrt{2^0}=1\);
\(\sqrt2=\sqrt2\);
\(\sqrt{2^2}=2\);
\(\sqrt{2^3}=2\sqrt2\);
\(\sqrt{2^{2017}}=2^{1008}\sqrt2\).

b)

\(\sqrt{10^{-5}}=\frac{\sqrt{10}}{1000}\);
\(\sqrt{10^{-4}}=\frac1{100}\);
\(\sqrt{10^{-3}}=\frac{\sqrt{10}}{100}\);
\(\sqrt{10^{-2}}=\frac1{10}\);
\(\sqrt{10^{-1}}=\frac{\sqrt{10}}{10}\).

Javob: a) \(\frac{\sqrt2}{2}, 1, \sqrt2, 2, 2\sqrt2, 2^{1008}\sqrt2\); b) \(\frac{\sqrt{10}}{1000}, \frac1{100}, \frac{\sqrt{10}}{100}, \frac1{10}, \frac{\sqrt{10}}{10}\).