Answer
$ x=-\displaystyle \frac{4}{5}$
Work Step by Step
$ 9^{x+2}=27^{-x}\qquad $ ... recognize $9$ and $27$ as powers of $3$
$(9^{2})^{x+2} =(3^{3})^{-x}\qquad $ ... apply: $(a^{m})^{n}=a^{mn}$
$3^{2x+4}=3^{-3x}\qquad $... If $ b^{M}=b^{N}$, then $ M=N $
$2x+4=-3x\qquad $...$/-4+3x $
$5x=-4 \qquad $...$/\div 5$
$ x=-\displaystyle \frac{4}{5}$
