Answer
$x=-\dfrac{1}{6}$
Work Step by Step
RECALL:
(i) If $a^M=a^N$, then $M=N.$
(ii) $\sqrt[n]{a} = a^{\frac{1}{n}}.$
(iii) $\dfrac{1}{a^m} = a^{-m}.$
Use rule (ii) to obtain
$9^x=\dfrac{1}{3^{\frac{1}{3}}}.$
Use rule (iii) to obtain
$9^x=3^{-\frac{1}{3}}.$
Write 9 as a power of 3 to obtain
$(3^2)^x=3^{-\frac{1}{3}}
\\3^{2x} = 3^{-\frac{1}{3}}.$
Use rule (i) above to obtain
$2x=-\dfrac{1}{3}.$
Solve the equation to obtain
$\dfrac{1}{2} \cdot 2x= -\dfrac{1}{3} \cdot \dfrac{1}{2}
\\x = -\dfrac{1}{6}.$
