Final answer:
To simplify the expression 3x² – 3x⁷/5x, the exponent rules for dividing terms with the same base are applied, and the numerical coefficients are divided accordingly. The options provided for the coefficient in the simplified expression are incorrect as they do not account for the changes to both the numerical coefficient and the exponent of x.
Step-by-step explanation:
When simplifying the expression 3x² – 3x⁷/5x, we first need to divide each term by 5x separately. For the second term 3x⁷/5x, we apply the rule of exponents mentioned, which is xᵗʷₗ = x(p+q), so we subtract the exponents (if they have the same base) in this case. After simplifying the second term, we subtract it from the first term to get the simplified expression. The coefficient in the simplified expression will be obtained after these operations.
For example, if we simplified the second term, it would have the same base x and the exponents would subtract, giving us a new exponent for x. However, the actual operation involves dividing 3x⁷ by 5x, resulting in a reduction of both the coefficient and the exponent of the x term. We need to remember that the exponent rule is applicable here, and we also need to apply the rules for dividing coefficients.
Ultimately, the simplified expression and its coefficient will depend on correctly applying the exponent rules and dividing coefficients. However, the possible coefficients presented in the options (5, 9, 3x, 5x) are not necessarily applicable since this simplification will affect both the numerical coefficient and the power of x.
Learn more about Simplifying expressions with exponents here: