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[tex]a^{\frac{1}{n}}=\sqrt[n]{a}\\\\a^n\cdot a^m=a^{n+m}\\\\a^{-1}=\dfrac{1}{a},\ a\neq0\\\\================[/tex]
[tex]a)\ 36^{\frac{1}{2}}=\sqrt{36}=6\\\\b)\ 9^{-\frac{1}{2}}=\left(\dfrac{1}{9}\right)^{\frac{1}{2}}=\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}\\\\c)\ 4^{1,5}=4^{1+0,5}=4^1\cdot4^{0,5}=4\cdot4^{\frac{1}{2}}=4\cdot\sqrt4=4\cdot2=8[/tex]
[tex]d)\ 0,16^{-\frac{3}{2}}=\left(\dfrac{16}{100}\right)^{-\frac{3}{2}}=\left(\dfrac{4}{25}\right)^{-\frac{3}{2}}=\left(\dfrac{25}{4}\right)^{1\frac{1}{2}}=\left(\dfrac{25}{4}\right)^{1+\frac{1}{2}}\\\\=\left(\dfrac{25}{4}\right)^1\cdot\left(\dfrac{25}{4}\right)^{\frac{1}{2}}=\dfrac{25}{4}\cdot\sqrt{\dfrac{25}{4}}=\dfrac{25}{4}\cdot\dfrac{5}{2}=\dfrac{125}{8}=15\dfrac{5}{8}[/tex]
[tex]e)\ \left(3\dfrac{3}{8}\right)^{\frac{4}{3}}=\left(\dfrac{27}{8}\right)^{1\frac{1}{3}}=\left(\dfrac{27}{8}\right)^{1+\frac{1}{3}}=\left(\dfrac{27}{8}\right)^1\cdot\left(\dfrac{27}{8}\right)^{\frac{1}{3}}\\\\=\dfrac{27}{8}\cdot\sqrt[3]{\dfrac{27}{8}}=\dfrac{27}{8}\cdot\dfrac{3}{2}=\dfrac{81}{16}=5\dfrac{1}{16}[/tex]
[tex]f)\ 9^{2\frac{1}{2}}=9^{2+\frac{1}{2}}=9^2\cdot9^{\frac{1}{2}}=81\cdot\sqrt9=81\cdot3=243\\\\g)\ 0,008^{-1\frac{1}{3}}=\left(\dfrac{8}{1000}\right)^{-1\frac{1}{3}}=\left(\dfrac{1}{125}\right)^{-1\frac{1}{3}}=125^{1\frac{1}{3}}=125^{1+\frac{1}{3}}\\\\=125^1\cdot125^{\frac{1}{3}}=125\cdot\sqrt[3]{125}=125\cdot5=625[/tex]
