Question

Самостоятельная работа по теме «Степень с рациональным показателем» Вариант 1

Answer 1

2. $(-2)^4=16$

3. $(1\frac{3}{8})^{-2}=(\frac{11}{8})^{-2}=\frac{64}{121}$

4. $8^{-\frac{2}{3}}=\frac{1}{\sqrt[3]{8^2}}=\frac{1}{2^2}=\frac{1}{4}$

5. $-2*27^{\frac{1}{3}}=-2*\sqrt[3]{27}=-2*3=-6$

6. $2^{-1}*64^{\frac{2}{3}}=\frac{1}{2}*\sqrt[3]{64^2}=\frac{1}{2}*4^2=\frac{1}{2}*16=8$

7. $(125^{-\frac{2}{3}}-16^{\frac{1}{2}}+343^{\frac{1}{3}}-3)^{-\frac{1}{2}}=(\frac{1}{\sqrt[3]{125^2}}-\sqrt{16}+\sqrt[3]{343}-3)^{-\frac{1}{2}}=\\=(\frac{1}{5^2}-4+7-3)^{-\frac{1}{2}}=(5^{-2})^{-\frac{1}{2}}=5$

8. $(3^{0.5}-5^{0.5})^2:((2-15^{0.25})(2+15^{0.25}))=\frac{3-2*3^{0.5}*5^{0.5}+5}{4-15^{0.5}}=\frac{8-2*15^{0.5}}{4-15^{0.5}}=\\=\frac{2*(4-15^{0.5})}{4-15^{0.5}}=2$

9. $\sqrt[3]{a^2}*\sqrt[6]{a^5}=a^{\frac{2}{3}}*a^{\frac{5}{6}}=a^{\frac{2}{3}+\frac{5}{6}}=a^{\frac{9}{6}}=a^{\frac{3}{2}}$

10. $\sqrt[6]{a}:\sqrt[8]{a^{-5}}=a^{\frac{1}{6}}:a^{-\frac{5}{8}}=a^{\frac{1}{6}+\frac{5}{8}}=a^{\frac{19}{24}}$

11. $(\sqrt[3]{a^2})^6=(a^2)^2=a^4$

12. $a^{\frac{1}{12}}*\sqrt[4]{a}=a^{\frac{1}{12}}*a^{\frac{1}{4}}=a^{\frac{1}{12}+\frac{1}{4}}=a^{\frac{1}{3}}$

13. $\sqrt{\sqrt[3]{a}}=\sqrt[6]{a}=a^{\frac{1}{6}}$

14. $(a\sqrt[3]{a^2b})^3=a^3*a^2b=a^5b$

15. $6ab\sqrt[9]{a^8b^3}:\frac{2a}{3b}*\sqrt[6]{a^2b^5}=\frac{6ab*a^{\frac{8}{9}}b^{\frac{1}{3}}*3b*a^{\frac{1}{3}}b^{\frac{5}{6}}}{2a}=9a^{\frac{8}{9}+\frac{1}{3}}b^{1+\frac{1}{3}+1+\frac{5}{6}}=9a^{\frac{11}{9}}b^{\frac{19}{6}}$