Question

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

Answer 1

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

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

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

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