Question

Which exponent rule(s) would be used to simplify this expression? 2x(5) ⋅ 12x(−4)
(1 point)
Responses

The quotient rule to subtract 2 - 12 = -10. You would also subtract the exponents to get 5 - 4 = 1 for the power of x.
The quotient rule to subtract 2 - 12 = -10. You would also subtract the exponents to get 5 - 4 = 1 for the power of x.

The negative exponent rule to get 5 - (-4) = 9 for the power of x and then multiply 2 x 12 = 24 for the coefficient.
The negative exponent rule to get 5 - (-4) = 9 for the power of x and then multiply 2 x 12 = 24 for the coefficient.

The power to power rule since you have two different exponents on the x, so the new exponent would be -20. Also, you would add 2 and 12 using the product rule for exponents.
The power to power rule since you have two different exponents on the x, so the new exponent would be -20. Also, you would add 2 and 12 using the product rule for exponents.

The product exponent rule to add 5 + -4 to get an exponent of 1 on the x. You would also multiply 2 x 12 since they are coefficients.

Answer 1

To simplify the expression \( 2x^5 \cdot 12x^{-4} \), the correct exponent rules to apply would be the **product of powers rule** and then also multiply the coefficients.

1. **Product of Powers Rule**: This rule states that when multiplying two expressions with the same base, you add the exponents. In this case:
\[
x^5 \cdot x^{-4} = x^{5 + (-4)} = x^{1}
\]

2. **Coefficients**: You also multiply the numerical coefficients:
\[
2 \cdot 12 = 24
\]

Putting it together, you would have:
\[
2x^5 \cdot 12x^{-4} = 24x^{1}
\]

So the correct response would be:
"The product exponent rule to add \(5 + (-4)\) to get an exponent of \(1\) on the \(x\). You would also multiply \(2 \cdot 12\) since they are coefficients."