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

The correct option is B 1

We have,

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

$\Rightarrow \frac{2^m\times 2^3\times 3^{2m}\times 5^m\times 5^n\times 5^3\times 6^n\times 6}{3^n\times 6^m\times 6\times {10}^n\times {10}^3\times {15}^m}$

$\Rightarrow \frac{2^m\times 2^3\times 3^{2m}\times 5^m\times 5^n\times 5^3\times {(2\times 3)}^n}{3^n\times {(2\times 3)}^m\times {10}^n\times {10}^3\times {(3\times 5)}^m}$

$\Rightarrow \frac{2^m\times 2^3\times 3^{2m}\times 5^m\times 5^n\times 5^3\times 2^n\times 3^n}{3^n\times 2^m\times 3^m\times {10}^n\times {10}^3\times 3^m\times 5^m}$

$\Rightarrow 1$

Hence, this is the answer.