Question

question
fully simplify using only positive exponents.
\\(\frac{3x^4y^8}{9x^6y^7}\\)

Explanation:

Step1: Simplify coefficients

Simplify the fraction of the coefficients: $\frac{3}{9}=\frac{1}{3}$.

Step2: Simplify \(x\)-terms

Use the rule \( \frac{a^m}{a^n}=a^{m - n} \) for \(x\): $\frac{x^4}{x^6}=x^{4 - 6}=x^{-2}=\frac{1}{x^2}$.

Step3: Simplify \(y\)-terms

Use the rule \( \frac{a^m}{a^n}=a^{m - n} \) for \(y\): $\frac{y^8}{y^7}=y^{8 - 7}=y^{1}=y$.

Step4: Combine all parts

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term: $\frac{1}{3}\times\frac{1}{x^2}\times y=\frac{y}{3x^2}$.

Answer:

$\frac{y}{3x^2}$