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

Question

options:

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

Answer 1

To simplify the expression \( 2x^5 \cdot 12x^{-4} \), we need to use the following exponent rules:

1. Product of Powers Rule: This rule states that when multiplying two powers with the same base, you add the exponents. In this case, you have \( x^5 \) and \( x^{-4} \). So, the exponents would be added: \( 5 + (-4) = 1 \).

2. Multiplication of Coefficients: You multiply the numerical coefficients \( 2 \) and \( 12 \) together.

Putting this together:

• Multiply the coefficients: \( 2 \cdot 12 = 24 \).
• Add the exponents: \( x^{5 + (-4)} = x^1 \).

Therefore, the expression simplifies to \( 24x^1 \) or simply \( 24x \).

The correct choice from the given options is:

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.