Simplify. Express your answer using exponents. (9n³p⁸)² Submit

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!