To simplify the expression \( 6x^4 \cdot 3^{x^2} \), let's break it down:
- Multiplication of coefficients: Multiply the numerical coefficients \( 6 \) and \( 3 \).
- 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:
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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.
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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.
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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.
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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.
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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.
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