Simplify. Express your answer using exponents. (12d³g⁸)²

To simplify ((12d³g⁸)²), we will use the power of a product rule and the power of a power rule for exponents.

1. Apply the power of a product rule:

((ab)^n = a^n b^n).

Here, (a = 12), (b = d³g⁸), and (n = 2).

So, we have:

[

(12d³g⁸)² = 12² cdot (d³)² cdot (g⁸)²

]

2. Calculate each part:

– (12² = 144)

– ((d³)² = d^{3 cdot 2} = d⁶)

– ((g⁸)² = g^{8 cdot 2} = g^{16})

3. Combine the results:

Putting it all together, we get:

[

144d⁶g^{16}

]

Thus, the simplified expression is (boxed{144d^6g^{16}}).