Question

Which exponent rule(s) would be used to simplify this expression?   2x^5⋅12x^−4 (1 point)ResponsesThe 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 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 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 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 \( 2x^5 \cdot 12x^{-4} \), you would use the following exponent rules:

1. Product Rule for Exponents: When multiplying like bases, you add the exponents. So for \( x^5 \cdot x^{-4} \), you would add the exponents: \[ 5 + (-4) = 1. \] This means \( x^5 \cdot x^{-4} = x^{1} \).

2. Multiplying Coefficients: You would multiply the coefficients \( 2 \) and \( 12 \): \[ 2 \cdot 12 = 24. \]

Putting it all together, the simplified expression would be: \[ 24x^1 \quad \text{or simply} \quad 24x. \]

Thus, the appropriate choice from your responses would be the one that mentions using the product exponent rule to add the exponents and multiplying the coefficients.