Question

To simplify this expression, 6x^4 ⋅ 3^x2
which would be the correct steps?(1 point)
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.

I know the options are not fully correct

Answer 1

To simplify the expression \( 6x^4 \cdot 3^{x^2} \), let's break it down:

1. **Multiplication of coefficients:** Multiply the numerical coefficients \( 6 \) and \( 3 \).
2. **Handling the variable:** The \( x \) terms maintain their exponent and do not combine with the exponent of \( 3^{x^2} \) since they are different bases.

Let's assess the provided options:

1. **Add 6 + 3 for the numbers; then multiply 2 x 4 to get the exponent for x.** - This is incorrect because you should multiply the coefficients, not add them.

2. **You cannot simplify this expression because these are not like terms.** - This option incorrectly states that simplification is not possible. While you can't combine the bases, you can simplify the coefficients.

3. **Multiply 6 x 3 for the numbers; then multiply 2 x 4 for the exponent on x.** - This is incorrect. You multiply the coefficients \( 6 \) and \( 3 \), but you do not multiply the exponents.

4. **Multiply 6 x 3 for the numbers; then add 2 + 4 for the exponent on x.** - This is incorrect. You multiply the coefficients but do not add exponents from different bases.

5. **Multiply 6 x 3 for the numbers; then add 2 + 4 for the exponent on x.** - This is also not correct for the same reason as above.

Since none of the options fully capture the correct simplification steps, here’s how it’s done correctly:

- Calculate \( 6 \cdot 3 = 18 \)
- The expression remains \( x^4 \) and \( 3^{x^2} \) as they cannot be combined.

Thus, the simplified expression is \( 18x^4 \cdot 3^{x^2} \). You can state that the final expression can no longer be simplified further.