Question

only positive exponents.
\frac{2xy^{8}}{2x^{3}y^{7}}

Explanation:

Step1: Simplify the coefficients

The coefficient of the numerator is 2 and the coefficient of the denominator is 2. So, $\frac{2}{2} = 1$.

Step2: Simplify the \(x\)-terms

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the \(x\)-terms: $\frac{x}{x^3}=x^{1 - 3}=x^{-2}$. Since we want only positive exponents, $x^{-2}=\frac{1}{x^2}$.

Step3: Simplify the \(y\)-terms

Using the same exponent rule, for the \(y\)-terms: $\frac{y^8}{y^7}=y^{8 - 7}=y^{1}=y$.

Step4: Combine the results

Multiply the results from Step1, Step2, and Step3: $1\times\frac{1}{x^2}\times y=\frac{y}{x^2}$.

Answer:

$\frac{y}{x^2}$