(a³-b⁴) ²

To simplify \((a^3 - b^4)^2\), we can use the formula for the square of a binomial, which states that \((x - y)^2 = x^2 - 2xy + y^2\).

Here, let \(x = a^3\) and \(y = b^4\). Applying the formula, we get:

\[ (a^3 - b^4)^2 = (a^3)^2 - 2(a^3)(b^4) + (b^4)^2 \]

Now, calculate each term:

1. \((a^3)^2 = a^{3 \cdot 2} = a^6\)
2. \((b^4)^2 = b^{4 \cdot 2} = b^8\)
3. \(-2(a^3)(b^4) = -2a^3b^4\)

Putting it all together:

\[ (a^3 - b^4)^2 = a^6 - 2a^3b^4 + b^8 \]

So the final result is:

\[ a^6 - 2a^3b^4 + b^8 \]