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