Simplify. Express your answer using exponents.
(9n³p⁸)²
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Simplify. Express your answer using exponents. (9n³p⁸)² Submit
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To simplify the expression ((9n³p⁸)²), we will apply the power of a product rule, which states that ((ab)^{m} = a^{m}b^{m}), and the power of a power rule, which is ((a^m)^{n} = a^{m cdot n}).
1. Start by squaring each component inside the parentheses:
[(9)², (n³)², (p⁸)²]
2. Calculate each:
– (9² = 81)
– ((n³)² = n^{3 cdot 2} = n^{6})
– ((p⁸)² = p^{8 cdot 2} = p^{16})
3. Combine these results:
[81n^{6}p^{16}]
Therefore, the simplified expression is:
[
boxed{81n^{6}p^{16}}
]
This result is in exponential form, as required! If you have more questions about exponents or other topics, feel free to ask!