To simplify the expression \((3m^2n^9p^9)^2\), we apply the power of a product property, which states that \((ab)^n = a^n \cdot b^n\).
So we can break it down as follows:
\[ (3m^2n^9p^9)^2 = 3^2 \cdot (m^2)^2 \cdot (n^9)^2 \cdot (p^9)^2 \]
Calculating each part:
- \(3^2 = 9\)
- \((m^2)^2 = m^{2 \cdot 2} = m^4\)
- \((n^9)^2 = n^{9 \cdot 2} = n^{18}\)
- \((p^9)^2 = p^{9 \cdot 2} = p^{18}\)
Now, combining these results gives:
\[ 9m^4n^{18}p^{18} \]
Thus, the simplified expression \((3m^2n^9p^9)^2\) is indeed equivalent to \(9m^4n^{18}p^{18}\).
Therefore, the statement is True.