Question

$\frac{16\times 32}{9\times 27\times 81}=?$

• A. ${\frac{2}{3}}^{12}$
• B. ${\frac{2}{3}}^{11}$
• C. ${\frac{2}{3}}^{13}$
• D. ${\frac{2}{3}}^9$
• E. $Noneofthese$

Answer 1

The correct option is D ${\frac{2}{3}}^9$

$Here,\frac{2^4\times 2^5}{3^2\times 3^3\times 3^4}\left[\begin{array}{cc}\because 16=2^4.32=2^5& \\ 9=3^2,27=3^3& \\ 81=3^4& \end{array}\right]$
By applying the rule of indices,
$\frac{2^9}{3^9}=(\frac{2}{3}{)}^9$