Answer
$729$
Work Step by Step
We want to break down this problem a little to be able to work with it. The number $243$ can be broken down into a small base raised to a power: $3^5$. Let us rewrite this number:
$(3^5)^{1.2}$
Raising a power to a power means we can multiply the two powers or exponents together:
$3^{(5)(1.2)}$
Multiply to simplify:
$3^{6}$
Simplify by raising the base to the specified power:
$729$