Question

The value of ${\left(\frac{2^m}{2^n}\right)}^r{\left(\frac{2^n}{2^r}\right)}^m{\left(\frac{2^r}{2^m}\right)}^n$ is

• A. 1
• B. 1/2
• C. 0
• D. -1

Answer 1

The correct option is A

1

$\begin{array}{c}{\left(\frac{2^m}{2^n}\right)}^r{\left(\frac{2^n}{2^r}\right)}^m{\left(\frac{2^r}{2^m}\right)}^n\\ =\frac{2^{mr}}{2^{nr}}.\frac{2^{mn}}{2^{mr}}.\frac{2^{nr}}{2^{mn}}=1.\end{array}$