fully simplify using only positive exponents. \n\\frac{8x^{8}y^{3}}{8x^{4}y^{7}}

Explanation:

Step1: Simplify the coefficient

Simplify (\frac{8}{8}) (\frac{8}{8}=1)

Step2: Use the quotient rule for exponents (a^m\div a^n=a^{m - n}) for (x) terms

For (x) terms: (x^8\div x^4=x^{8 - 4}) (x^{8 - 4}=x^4)

Step3: Use the quotient rule for exponents (a^m\div a^n=a^{m - n}) for (y) terms

For (y) terms: (y^3\div y^7=y^{3 - 7}) Since (y^{3-7}=y^{-4}=\frac{1}{y^{4}}) (using (a^{-n}=\frac{1}{a^{n}}))

Step4: Combine the results

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

Answer:

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