Question

The value of $\frac{(64{)}^{-1/6}\times (216{)}^{-1/3}\times (81{)}^{1/4}}{(512{)}^{12}\times (16{)}^{1/4}\times (9{)}^{-1/2}}$ is

• A. $3$
• B. $6$
• C. $1$
• D. None of these

Answer 1

The correct option is A $3$

$\frac{(64{)}^{-1/6}\times (216{)}^{-1/3}\times (81{)}^{1/4}}{(512{)}^{12}\times (16{)}^{1/4}\times (9{)}^{-1/2}}$

$=\frac{2^{6\times \frac{-1}{6}}\times 6^{3\times \frac{-1}{3}}\times 3^{4\times \frac{1}{4}}}{8^{3\times \frac{-1}{3}}\times 2^{4\times \frac{1}{4}}\times 3^{2\times \frac{-1}{2}}}$

$=\frac{2^{-1}\times 6^{-1}\times 3}{8^{-1}\times 2^1\times 3^{-1}}$

$=\frac{8\times 3\times 3}{2\times 6\times 2}=\frac{72}{24}=3$