Question

solve x:81^-2÷729^1-x=9^2x​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

Given(81)−1(729)1−x=92x\begin{lgathered}Given \\\frac{(81)^{-1}}{(729)^{1-x}}=9^{2x}\end{lgathered}

Given

(729)

1−x

(81)

−1

=9

2x

⟹(92)−1(93)1−x=92x\implies \frac{(9^{2})^{-1}}{(9^{3})^{1-x}}=9^{2x}⟹

(9

3

)

1−x

(9

2

)

−1

=9

2x

⟹92×(−1)93×(1−x)=92x\implies \frac{9^{2\times (-1)}}{9^{3\times (1-x)}}=9^{2x}⟹

9

3×(1−x)

9

2×(−1)

=9

2x

ByExponentialLaw,(am)n=amn\begin{lgathered}By \: Exponential \:Law,\\(a^{m})^{n}=a^{mn}\end{lgathered}

ByExponentialLaw,

(a

m

)

n

=a

mn