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

Question

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 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.
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.

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.

Answer 1

To simplify the expression \(2x^5 \cdot 12x^{-4}\), the appropriate rules for exponents to use are as follows:

1. Product Rule: When multiplying two expressions with the same base, you add the exponents. In this case, you have exponents of \(x^5\) and \(x^{-4}\). So you would add \(5 + (-4) = 1\).

2. Multiplying Coefficients: You also multiply the coefficients \(2\) and \(12\).

Thus, the correct choice is:

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

So the simplified expression would be \(24x^1\) or simply \(24x\).