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

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.

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 first option is the correct answer. The product rule for exponents would be used to multiply the coefficients (2 and 12) and add the exponents of the variable (5 and -4), resulting in the simplified expression of 24x.

u sure?

Apologies for the confusion in my previous response. You are correct, the product rule for exponents would not be used in this case. The correct approach would be to use the product rule to multiply the coefficients (2 and 12) and then add the exponents of the variable (5 and -4). This would simplify the expression to 24x^1, or simply 24x.