Definitions
The marking [[$ (3^2)^4 $]] stands for the power of a power. The exponent is the number 4 and the base number is the number inside the brackets, i.e. [[$3^2$]]. Let us consider the power as a base number like a single number. The power expression can be written as follows:
[[$ (3^2)^4 = \underbrace{3^2 \cdot 3^2 \cdot 3^2 \cdot 3^2}_{\text{This is a product of powers with the same base that is already known.}} = 3 \overbrace{^{2+2+2+2}}^{=2 \cdot 4} =3^8 $]]
[[$ \left(a^m\right)^n = a^{m \cdot n}$]]
[[$ (3^2)^4 = \underbrace{3^2 \cdot 3^2 \cdot 3^2 \cdot 3^2}_{\text{This is a product of powers with the same base that is already known.}} = 3 \overbrace{^{2+2+2+2}}^{=2 \cdot 4} =3^8 $]]
The power of a power
A power is raised to a power by multiplying the exponents. The base stays the same.[[$ \left(a^m\right)^n = a^{m \cdot n}$]]