Question

The value of $\frac{2^{m+3}\times 3^{2m-n}\times 5^{m+n+3}\times 6^{n+1}}{6^{m+1}\times {10}^{n+3}\times {15}^m}$ is equal to

• A. 0
• B. 1
• C. $2^m$
• D. None of these

Answer 1

The correct option is B 1

$\frac{2^{m+3}\times 3^{2m-n}\times 5^{m+n+3}\times 6^{n+1}}{6^{m+1}\times {10}^{n+3}\times {15}^m}$

(Split numbers in there prime factors)

$\Rightarrow \frac{2^{m+3}\times 3^{2m-n}\times 5^{m+n+3}\times 2^{n+1}\times 3^{n+1}}{2^{m+1}\times 3^{m+1}+2^{n+3}\times 5^{n+3}\times 3^m\times 5^m}$

$\frac{2^{m+n+4}\times 3^{2m+1}\times 5^{m+n+3}}{2^{m+n+4}\times 3^{2m+1}\times 5^{m+n+3}}$

$\Rightarrow 1$