Identify the formula for the volume of a cube

The volume $V$ of a cube with side length $a$ is calculated using the formula:

$V = a^3$

Substitute the given side length

Given $a = 6xyz^2$, substitute this into the volume formula:

$V = (6xyz^2)^3$

Perform the exponentiation

Apply the power rule $(abc)^n = a^n b^n c^n$. First, calculate $6^3 = 6 \times 6 \times 6 = 216$. Then, cube the variables: $x^3$, $y^3$, and $(z^2)^3 = z^{2 \times 3} = z^6$.

$V = 6^3 \cdot x^3 \cdot y^3 \cdot (z^2)^3 = 216x^3y^3z^6$