Question 104905
{{{(9^(2x))*(27^(x-3))=1/9}}}
Use the exponentiation rules
{{{(x^m)^n=x^(m*n)}}}
{{{(x^m)*(x^n)=x*(m+n)}}}
Let's start. 
{{{((3^2)^(2x)*(3^3)^(x-3))=3^(-2) }}}Convert to the same base, 3.
{{{3^(4x)*(3^(3(x-3)))=3^(-2) }}}Use the rules. 
{{{3^(4x+(3(x-3)))=3^(-2) }}}Simplify. 
{{{4x+3(x-3)=-2}}}Inverse function.
{{{4x+3x-9=-2}}}Distribute. 
{{{7x-9=-2}}}Additive inverse. 
{{{7x=7}}}Multiplicative inverse. 
{{{x=1}}}
Verify the solution. 
{{{(9^(2x))*(27^(x-3))=1/9}}}
{{{(9^(2))*(27^(1-3))=1/9}}}
{{{(81/729)=1/9}}}
{{{(1/9)=1/9}}}
Good answer.