Question

fully simplify using only positive exponents.\\(\frac{2x^7y^3}{x^6y^5}\\)

Explanation:

Step1: Simplify the coefficient and \(x\)-terms

The coefficient is \(2\) (remains as is). For the \(x\)-terms, use the rule \( \frac{x^m}{x^n}=x^{m - n} \). So \( \frac{x^7}{x^6}=x^{7 - 6}=x^1 = x \).

Step2: Simplify the \(y\)-terms

For the \(y\)-terms, use the same exponent rule: \( \frac{y^3}{y^5}=y^{3 - 5}=y^{-2} \). But we need positive exponents, so \(y^{-2}=\frac{1}{y^2}\).

Step3: Combine the results

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

Answer:

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