Answer
$\dfrac{1}{27}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $a^{mn}= (a^m)^n$
Note that $3x=-x(-3)$
Thus,
$5^{3x} = 5^{-x(-3)}$
Use rule (2) above to obtain:
$5^{-x(-3)} = (5^{-x})^{-3}$
With $5^{-x} = 3$, the expression above is equivalent to:
$(5^{-x})^{-3} = 3^{-3}$
Use rule (1) above to obtain:
$3^{-3} = \dfrac{1}{3^3} = \dfrac{1}{27}$
Thus,
$5^{3x} = \dfrac{1}{27}$
