Question

Solve for $x:{81}^{-2}÷{729}^{1-x}=9^{2x}$

• A. $2$
• B. $-2$
• C. $7$
• D. $-7$

Answer 1

The correct option is C $7$

${81}^{-2}÷{729}^{1-x}=9^{2x}$

$\frac{{81}^{-2}}{{729}^{1-x}}=9^{2x}$

$\frac{{\left(9^2\right)}^{-2}}{{\left(9^3\right)}^{1-x}}=9^{2x}$

$\frac{9^{-4}}{9^{3(1-x)}}=9^{2x}$

$9^{-4}=9^{3-3x}{.9}^{2x}$

$9^{-4}=9^{3-3x+2x}$

$9^{-4}=9^{3-x}$

Comparing both side

Then,

$-4=3-x$

$-4-3=-x$

$-7=-x$

$x=7$

Hence, it is required solution.