Question

If $\frac{6^{-4}\times {12}^3\times 36}{3^{-5}\times {18}^2}=m$ then $m=$?

• A. $6$
• B. $4$
• C. $36$
• D. $64$

Answer 1

Answer: (C)

$36$

$\frac{6^{-4}\times {12}^3\times 36}{3^{-5}\times {18}^2}=\frac{{(2\times 3)}^{-4}\times {(2^2\times 3)}^3\times (2^2\times 3^2)}{3^{-5}\times {(2\times 3^2)}^2}$
$=\frac{2^{-4}\times 3^{-4}\times 2^6\times 3^3\times 2^2\times 3^2}{3^{-5}\times 2^2\times 3^4}$
$=\frac{2^{-4+6+2}\times 3^{-4+3+2}}{3^{-5+4}\times 2^2}$
$=\frac{2^4\times 3}{3^{-1}\times 2^2}$
$=2^{4-2}\times 3^{1-(-1)}$
$=2^2\times 3^2$
$=4\times 9$
$=36$
$\therefore m=36$