Question

What is the value of $‘‘x"$ in the expression $(\frac{11}{9}{)}^3\times (\frac{9}{11}{)}^6=(\frac{11}{9}{)}^{2x-1}$?

• A. $1$
• B. $-1$
• C. $0$
• D. None of the above

Answer 1

The correct option is B $-1$

$(\frac{11}{9}{)}^3\times (\frac{9}{11}{)}^6=(\frac{11}{9}{)}^{2x-1}$

$⟹(\frac{11}{9}{)}^3\times (\frac{11}{9}{)}^{-6}=(\frac{11}{9}{)}^{2x-1}$

$⟹(\frac{11}{9}{)}^{3+(-6)}=(\frac{11}{9}{)}^{2x-1}$

$⟹(\frac{11}{9}{)}^{-3}=(\frac{11}{9}{)}^{2x-1}$

$⟹-3=2x-1$

$⟹-3+1=2x$

$⟹\frac{-2}{2}=x$

$⟹x=-1$