Question

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

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

Answer 1

Answer: (B)

1

Numerator $=2^{m+3}\cdot 3^{2m-n}\cdot 5^{m+n+3}\cdot 2^{n+1}\cdot 3^{n+1}$
$=2^{m+n+4}\cdot 3^{2m+1}\cdot 5^{m+n+3}$ (i)
Denominator $=2^{m+1}\cdot 3^{m+1}\cdot 2^{n+3}\cdot 5^{n+3}\cdot 3^m\cdot 5^m$
$=2^{m+n+4}\cdot 3^{2m+1}\cdot 5^{m+n+3}$ (ii)
Given expression $=1$