Question

Evaluate

$(\frac{a^m}{a^{-n}}{)}^{m-n}\times (\frac{a^n}{a^{-l}}{)}^{n-l}\times (\frac{a^l}{a^{-m}}{)}^{l-m}$

• A. 0
• B. a
• C. 1
• D. 2

Answer 1

The correct option is C

1

Given

$(\frac{a^m}{a^{-n}}{)}^{m-n}\times (\frac{a^n}{a^{-l}}{)}^{n-l}\times (\frac{a^l}{a^{-m}}{)}^{l-m}$

$\because \frac{a^x}{a^y}=a^{(x-y)}$

$\Rightarrow$ $(a^{m+n}{)}^{m-n}\times (a^{n+l}{)}^{n-l}\times (a^{l+m}{)}^{l-m}$

$\Rightarrow$ $\left(a^{m^2-n^2}\right)\times \left(a^{n^2-l^2}\right)\times \left(a^{l^2-m^2}\right)$

$\because a^x\times a^y=a^{(x+y)}$

Now, we get

$a^{m^2-n^2+n^2-l^2+l^2-m^2}$ $\Rightarrow$ $a^0=1$