$1) {48}^0, {10}^{—2}, {\left(\frac{2}{3}\right)}^{—1}, {\left(0,3\right)}^{—3}, {\left(—1,2\right)}^{—2}, {\left(2\frac{1}{4}\right)}^{—2}.$

Воспользуемся свойством степеней

$a^0=1.$ ${48}^0=1$

Воспользуемся свойством степеней

$a^{—n}=\frac{1}{a^n}.$ ${10}^{—2}=\frac{1}{{10}^2}=\frac{1}{100}=0,01$ ${\left(\frac{2}{3}\right)}^{—1}=\frac{1}{\left({\displaystyle \frac{2}{3}}\right)}=1:\frac{2}{3}=1·\frac{3}{2}=\frac{3}{2}=1,5$ ${\left(0,3\right)}^{—3}=\frac{1}{{\left(0,3\right)}^3}=\frac{1}{0,027}=\frac{1·1000}{0,027·1000}=\frac{1000}{27}=37\frac{1}{27}$ ${\left(—1,2\right)}^{—2}=\frac{1}{{\left(—1,2\right)}^3}=\frac{1}{1,44}=\frac{1·100}{1,44·100}=\frac{100}{144}=\frac{25}{36}$

${\left(2\frac{1}{4}\right)}^{—2}={\left(\frac{2·4+1}{4}\right)}^{—2}={\left(\frac{9}{4}\right)}^{—2}=\frac{1}{{\left({\displaystyle \frac{9}{4}}\right)}^2}=\frac{1}{\left({\displaystyle \frac{81}{16}}\right)}=1:\frac{81}{16}=1·\frac{16}{81}=\frac{16}{81}.$ $2) \sqrt[3]{27}, \sqrt[4]{81}, \sqrt[5]{32}, \sqrt[6]{8^2}, \sqrt[8]{{16}^2}, \sqrt[3]{{27}^2}.$

Воспользуемся свойством корней

$\sqrt[n]{a^m}=a^{\frac{m}{n}}$

и свойством степеней

${\left(a^n\right)}^m=a^{n·m}.$ $\sqrt[3]{27}={27}^{\frac{1}{3}}={\left(3^3\right)}^{\frac{1}{3}}=3^{3·\frac{1}{3}}=3^1=3$ $\sqrt[4]{81}={81}^{\frac{1}{4}}={\left(3^4\right)}^{\frac{1}{4}}=3^{4·\frac{1}{4}}=3^1=3$ $\sqrt[5]{32} ={32}^{\frac{1}{5}}={\left(2^5\right)}^{\frac{1}{5}}=2^{5·\frac{1}{5}}=2^1=2$ $\sqrt[6]{8^2} =\sqrt[6]{{\left(2^3\right)}^2}=\sqrt[6]{2^{3·2}}=\sqrt[6]{2^6}={\left(2^6\right)}^{\frac{1}{6}}=2^{6·\frac{1}{6}}=2^1=2$ $\sqrt[8]{{16}^2}=\sqrt[8]{{\left(2^4\right)}^2}=\sqrt[8]{2^{4·2}}=\sqrt[8]{2^8}={\left(2^8\right)}^{\frac{1}{8}}=2^{8·\frac{1}{8}}=2^1=2$ $\sqrt[3]{{27}^2}=\sqrt[3]{{\left(3^3\right)}^2}=\sqrt[3]{3^{3·2}}=\sqrt[3]{3^6}={\left(3^6\right)}^{\frac{1}{3}}=3^{6·\frac{1}{3}}=3^2=9.$

Воспользуемся свойствами степеней

${\left(a^n\right)}^m=a^{n·m}, a^{—n}=\frac{1}{a^n}.$ $8^{\frac{1}{3}}={\left(2^3\right)}^{\frac{1}{3}}=2^{3·\frac{1}{3}}=2^1=2$ ${27}^{\frac{2}{3}}={\left(3^3\right)}^{\frac{2}{3}}=3^{3·\frac{2}{3}}=3^2=9$ ${10000}^{\frac{1}{4}}={\left({10}^4\right)}^{\frac{1}{4}}={10}^{4·\frac{1}{4}}={10}^1=10$ ${32}^{\frac{2}{5}}={\left(2^5\right)}^{\frac{2}{5}}=2^{5·\frac{2}{5}}=2^2=4$ ${32}^{—\frac{3}{5}}={\left(2^5\right)}^{—\frac{3}{5}}=2^{5·\left(—\frac{3}{5}\right)}=2^{—3}=\frac{1}{2^3}=\frac{1}{8}=0,125$ ${\left(\frac{27}{64}\right)}^{\frac{2}{3}}={\left({\left(\frac{3}{4}\right)}^3\right)}^{\frac{2}{3}}={\left(\frac{3}{4}\right)}^{3·\frac{2}{3}}={\left(\frac{3}{4}\right)}^2=\frac{9}{16}=0,5625.$