Question

Using the properties of exponents, simplify the expression. (1 point)
(3p3n2)4=
(
3
𝑝
3
𝑛
2
)
4
=

Answer 1

To simplify the expression \((3p^{3}n^{2})^{4}\) using the properties of exponents, we apply the power of a product property and the power of a power property.

The power of a product property states that \((ab)^n = a^n b^n\), and the power of a power property states that \((a^m)^n = a^{m \cdot n}\).

Using these properties, we can simplify the expression step-by-step:

\[
(3p^{3}n^{2})^{4} = 3^{4} \cdot (p^{3})^{4} \cdot (n^{2})^{4}
\]

Now we simplify each part:

1. \(3^{4} = 81\)
2. \((p^{3})^{4} = p^{3 \cdot 4} = p^{12}\)
3. \((n^{2})^{4} = n^{2 \cdot 4} = n^{8}\)

Putting it all together, we have:

\[
(3p^{3}n^{2})^{4} = 81p^{12}n^{8}
\]

So the simplified expression is:

\[
\boxed{81p^{12}n^{8}}
\]