Câu 4:
\(\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdot\sqrt{x}}}}:x^{\frac{11}{16}}\)
\(=\sqrt{x\cdot\sqrt{x\cdot\sqrt{x\cdot x^{\frac12}}}}:x^{\frac{11}{16}}\)
\(=\sqrt{x\cdot\sqrt{x\cdot\sqrt{x^{\frac32}}}}:x^{\frac{11}{16}}\)
\(=\sqrt{x\cdot\sqrt{x\cdot x^{\frac32\cdot\frac12}}}:x^{\frac{11}{16}}\)
\(=\sqrt{x\cdot\sqrt{x\cdot x^{\frac34}}}:x^{\frac{11}{16}}\)
\(=\sqrt{x\cdot\sqrt{x^{\frac74}}}:x^{\frac{11}{16}}\)
\(=\sqrt{x\cdot x^{\frac74\cdot\frac12}}:x^{\frac{11}{16}}=\sqrt{x\cdot x^{\frac78}}:x^{\frac{11}{16}}=\sqrt{x^{\frac{15}{8}}}:x^{\frac{11}{16}}=x^{\frac{15}{16}-\frac{11}{16}}=x^{\frac{4}{16}}=x^{\frac14}=\sqrt[4]{x}\)
=>Chọn A
Câu 2:
\(a^{\frac23}\cdot\sqrt{a}=a^{\frac23}\cdot a^{\frac12}=a^{\frac23+\frac12}=a^{\frac76}\)
=>x=7/6
\(\sqrt[3]{b\cdot\sqrt{b\cdot\sqrt{b}}}=\sqrt[3]{b\cdot\sqrt{b\cdot b^{\frac12}}}=\sqrt[3]{b\cdot\sqrt{b^{\frac32}}}=\sqrt[3]{b\cdot b^{\frac34}}=\sqrt[3]{b^{\frac74}}\)
\(=b^{\frac74\cdot\frac13}=b^{\frac{7}{12}}\)
=>y=7/12
6x+12y=7+7=14
=>Chọn C
Câu 3:
\(\sqrt[21]{a^5}>\sqrt[7]{a^2}\)
=>\(a^{\frac{5}{21}}>a^{\frac27}\)
=>\(a^5>a^6\)
=>\(a^5-a^6>0\)
=>\(a^5\left(1-a\right)>0\)
=>\(a^5\left(a-1\right)<0\)
=>0<a<1
=>Chọn B
