To simplify the expression \(6x^4 \cdot 3^{x^2}\), the correct steps would involve multiplying the numeric coefficients and addressing the exponent on \(x\) properly.
The best response would be:
Multiply 6 x 3 for the numbers; then keep the exponent \(x^4\) as it is and multiply \(3^{x^2}\) since \(3^{x^2}\) is not like terms with \(x\). You cannot combine or add exponents because they are not directly related.
So to clarify:
- Multiply the coefficients: \(6 \cdot 3 = 18\)
- Keep \(x^4\) and \(3^{x^2}\) as they are.
The simplified form is \(18x^4 \cdot 3^{x^2}\), but no further simplification can be done because \(x^4\) and \(3^{x^2}\) are not like terms.
If we're looking for wording that aligns closest to the options provided, we select:
Multiply 6 x 3 for the numbers; then keep the exponent \(x^4\) as it is and do not change \(3^{x^2}\).
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