notation - What is the reasoning behind this exponents question?

What is $3^{3^{3}}?$

Plugging $3^{3^{3}}$into the calculator gives 7625597484987.
I believe because this implies that
$3^{3^{3}}=3^{27}$, is this true?

And plugging $(3^{3})^{3}$ gives 19683, because $(3^{3})^{3}=3^{3}\times 3^{3}\times 3^{3}=3^{9}=19683$

So which one is the correct answer, and why?

Answer

Remember the order of operations. Please Excuse My Dear Aunt Sally

Parentheses EXPONENTS Multiply and Divide and finally Addition and Subtraction.

So $3^{3^3}$ has Exponents of Exponents which means the ${b^c}$ of $a^{b^c}$ is evaluated first.