Question

Simplify:$\frac{9^{\frac{1}{3}\times {27}^{\frac{1}{2}}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}$

• A. $\sqrt{3}$
• B. $(3{)}^{-\frac{1}{3}}$
• C. $3^2$
• D. $3^{\frac{1}{2}}$

Answer 1

The correct option is C

$3^2$

$\frac{9^{\frac{1}{3}\times {27}^{\frac{1}{2}}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}=\frac{9^{\frac{1}{3}\times 3^{\frac{2}{3}}}}{3^{\frac{1}{6}}\times {27}^{\frac{1}{2}}}=\frac{(3^2{)}^{\frac{1}{3}\times 3^{\frac{2}{3}}}}{3^{\frac{1}{6}}\times (3^3{)}^{\frac{1}{2}}}=\frac{3^{\frac{2}{3}+\frac{2}{3}}}{3^{\frac{1}{6}+\frac{3}{2}}}=\frac{3^{\frac{4}{3}}}{3^{\frac{1+9}{6}}}=\frac{3^{\frac{4}{3}}}{3^{\frac{10}{6}}}=\frac{3^{\frac{4}{3}}}{3^{\frac{5}{3}}}=3^{\frac{4}{3}-\frac{5}{3}}=(3{)}^{-\frac{1}{3}}$