Question

simplify.
\\(\frac{6x^{7}}{2x^{5}}\\)

Explanation:

Step1: Apply exponent rule for division

When dividing terms with the same base, we subtract the exponents. For \( \frac{6x^{7}}{2x^{5}} \), we can separate the coefficients and the variables: \( \frac{6}{2} \times \frac{x^{7}}{x^{5}} \).

Step2: Simplify the coefficient and the variable

Simplify the coefficient: \( \frac{6}{2} = 3 \). For the variable part, using the rule \( \frac{x^{m}}{x^{n}} = x^{m - n} \), we have \( \frac{x^{7}}{x^{5}} = x^{7 - 5} = x^{2} \).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part: \( 3 \times x^{2} = 3x^{2} \).

Answer:

\( 3x^{2} \)