Answer
$x = \dfrac{4}{9}$
Work Step by Step
Rewrite terms so that they have common bases:
$(3^{3})^{3x} = 3^{4}$
Use the Power Property of Exponents, which says that when a power is raised to a power, multiply the exponents, keeping the base as-is:
$3^{9x} = 3^{4}$
If two numbers having the same base are equal, then their exponents are also equal; therefore, set the exponents equal to one another:
$9x = 4$
Divide both sides of the equation by $9$:
$x = \dfrac{4}{9}$
