Question

fully simplify using only positive exponents. \\(\frac{4x^5y^3}{2x^6y}\\)

Explanation:

Step1: Simplify the coefficient

Divide the coefficient \(4\) by \(2\): \(\frac{4}{2} = 2\)

Step2: Simplify the \(x\)-terms

Use the exponent rule \(\frac{a^m}{a^n}=a^{m - n}\) for \(x\)-terms: \(\frac{x^5}{x^6}=x^{5 - 6}=x^{-1}=\frac{1}{x}\) (but we will keep it as \(x^{-1}\) for now and handle positive exponents later)

Step3: Simplify the \(y\)-terms

Use the exponent rule \(\frac{a^m}{a^n}=a^{m - n}\) for \(y\)-terms: \(\frac{y^3}{y}=y^{3 - 1}=y^2\)

Step4: Combine and convert to positive exponents

Combine the results: \(2\times x^{-1}\times y^2=\frac{2y^2}{x}\) (since \(x^{-1}=\frac{1}{x}\))

Answer:

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