To simplify the expression \((3m^2n^9p^9)^2\), we need to apply the power of a product rule and the power of a power rule in exponents.
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The expression can be expanded using the power of a product: \((a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n\).
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Therefore: \[ (3m^2n^9p^9)^2 = 3^2 \cdot (m^2)^2 \cdot (n^9)^2 \cdot (p^9)^2 \]
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Now we compute each part:
- \(3^2 = 9\)
- \((m^2)^2 = m^{2 \cdot 2} = m^4\)
- \((n^9)^2 = n^{9 \cdot 2} = n^{18}\)
- \((p^9)^2 = p^{9 \cdot 2} = p^{18}\)
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Putting it all together: \[ (3m^2n^9p^9)^2 = 9m^4n^{18}p^{18} \]
Thus, the original expression simplifies correctly to \(9m^4n^{18}p^{18}\).
The statement in the question is True.
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