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

Question

(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."