Question

Evaluate the following:

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

• A. 1
• B. a
• C. 0
• D. 2

Answer 1

The correct option is A

1

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

$=(a^{m+n}{)}^{m-n}\times (a^{n+l}{)}^{n-l}\times \left(a^{l+m}{)}^{l-m}\right[Using\frac{k^x}{k^y}=k^{x-y}]$

$=(a{)}^{m^2-n^2}\times (a{)}^{n^2-l^2}\times \left(a{)}^{l^2-m^2}\right[Using{\left(k^x\right)}^y=k^{xy}andUsing(x+y)(x-y)=x^2-y^2]$

Adding all the powers we get
$=a^{m^2-n^2+n^2-l^2+l^2-m^2}(\because k^x\times k^y=k^{x+y})=a^0=1$