fully simplify using only positive exponents. \n\\frac{3x^{8}y^{7}}{6x^{6}y^{3}}

Explanation:

Step1: Simplify the coefficient

Divide (3) by (6). (\frac{3}{6}=\frac{1}{2})

Step2: Simplify the (x) - terms

Use the rule (\frac{a^{m}}{a^{n}}=a^{m - n}). For (x) terms, (m = 8) and (n=6), so (\frac{x^{8}}{x^{6}}=x^{8 - 6}=x^{2})

Step3: Simplify the (y) - terms

Use the rule (\frac{a^{m}}{a^{n}}=a^{m - n}). For (y) terms, (m = 7) and (n = 3), so (\frac{y^{7}}{y^{3}}=y^{7-3}=y^{4})

Step4: Combine the simplified parts

Multiply the simplified coefficient, (x) - term and (y) - term together. (\frac{1}{2}\times x^{2}\times y^{4}=\frac{x^{2}y^{4}}{2})

Answer:

(\frac{x^{2}y^{4}}{2})