Question

The value of

$\frac{9^x{\left(9^{x-1}\right)}^x}{9^{x+1}\cdot 3^{2x-2}}{\left\{\frac{{729}^{\frac{x}{3}}}{81}\right\}}^{-x}÷\frac{3^a-2^3\cdot 3^{a-2}}{3^a-3^{a-1}}$ is:

• A. $9$
• B. $6$
• C. $12$
• D. $16$

Answer 1

The correct option is B $6$

Given exp

$=\frac{9^x{\left(9^{x-1}\right)}^x}{9^{x+1}\cdot 3^{2x-2}}{\left\{\frac{{729}^{\frac{x}{3}}}{81}\right\}}^{-x}÷\frac{3^a-2^3\cdot 3^{a-2}}{3^a-3^{a-1}}$

$=\frac{3^{2x}(3^{2x-2}{)}^x}{3^{2x+2}{.3}^{2x-x}}{\left\{\frac{(3^6{)}^{\frac{x}{3}}}{3^4}\right\}}^{-x}÷\frac{3^{a-2}(3^2-2^3)}{3^{a-1}(3-1)}$

$=\frac{3^{2x}{.3}^{2x^2-2x}}{3^{2x+2+2x-2}}{\left\{\frac{3^{2x}}{3^4}\right\}}^{-x}÷\frac{3^{a-2-a+1}\times (9-8)}{2}$

$=\frac{3^{2x^2}}{3^{4x}}(3^{2x-4}{)}^{-x}÷\frac{1}{2\times 3}$

$=3^{2x^2-4x}\times 3^{-2x^2+4x}÷\frac{1}{6}$

$=3^0\times 6=1\times 6=6$