\(
\eqalign{
& 27^{ - \frac{x}
{3}} + 81^{\frac{{1 - x}}
{4}} = \cr
& \left( {3^3 } \right)^{ - \frac{x}
{3}} + \left( {3^4 } \right)^{\frac{{1 - x}}
{4}} = \cr
& 3^{3 \cdot - \frac{x}
{3}} + 3^{4 \cdot \frac{{1 - x}}
{4}} = \cr
& 3^{ - x} + 3^{1 - x} = \cr
& 3^{ - x} + 3 \cdot 3^{ - x} = \cr
& 4 \cdot 3^{ - x} = \cr
& \frac{4}
{{3^x }} \cr}
\)
