To simplify this expression, 6x^4 ⋅ 3^x2

Question

which would be the correct steps?

Responses:

Add 6 + 3 for the numbers; then multiply 2 x 4 to get the exponent for x.
Add 6 + 3 for the numbers; then multiply 2 x 4 to get the exponent for x.

You cannot simplify this expression because these are not like terms.
You cannot simplify this expression because these are not like terms.

Multiply 6 x 3 for the numbers; then multiply 2 x 4 for the exponent on x.
Multiply 6 x 3 for the numbers; then multiply 2 x 4 for the exponent on x.

Multiply 6 x 3 for the numbers; then add 2 + 4 for the exponent on x.
Multiply 6 x 3 for the numbers; then add 2 + 4 for the exponent on x.

Answer 1

To simplify the expression \(6x^4 \cdot 3^{x^2}\), you need to follow these steps:

1. Multiply the coefficients (the numerical parts): Multiply \(6\) and \(3\).
2. Examine the variables: The term \(x^4\) remains as is because \(3^{x^2}\) does not have the variable \(x\) in a form that could change \(x^4\).
3. Combine if applicable: The expression consists of different types of terms and cannot be combined further as they are not like terms.

Given the provided responses, the most suitable one would be:

Multiply 6 x 3 for the numbers; then keep \(x^4\) and \(3^{x^2}\) separate since they are not like terms.

This indicates the multiplication of the coefficients while also retaining the variables in their respective forms without implying further addition or multiplication of exponents incorrectly. However, since that exact response isn't listed, the best close option would be:

Multiply 6 x 3 for the numbers; then keep the \(x^4\) as is since the \(3^{x^2}\) is separate.

But from the options given, none are fully correct. The more typical correct outcome should specify multiplying 6 x 3 and leaving \(x^4\) and \(3^{x^2}\) as they are.