To simplify the expression [tex]\((3x)^4\)[/tex], we can use the property of exponents known as the power of a product property. This property states that [tex]\((a \cdot b)^m = a^m \cdot b^m\)[/tex].
Here are the steps to follow:
1. Identify the components:
The given expression is [tex]\((3x)^4\)[/tex], where [tex]\(3\)[/tex] is a constant and [tex]\(x\)[/tex] is a variable.
2. Apply the power to each component:
According to the power of a product property,
[tex]\[
(3x)^4 = 3^4 \cdot x^4
\][/tex]
3. Calculate [tex]\(3^4\)[/tex]:
To find [tex]\(3^4\)[/tex], multiply [tex]\(3\)[/tex] by itself 4 times:
[tex]\[
3^4 = 3 \times 3 \times 3 \times 3 = 81
\][/tex]
4. Combine the results:
After raising both the constant and the variable to the power of 4, we get:
[tex]\[
3^4 \cdot x^4 = 81 \cdot x^4
\][/tex]
Therefore, the correct simplification of the expression [tex]\((3x)^4\)[/tex] is:
[tex]\[
81x^4
\][/tex]
The correct answer is [tex]\(\boxed{81x^4}\)[/tex].
