Question

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

Explanation:

Step1: Split into coefficient & variables

$\frac{2x^7y^3}{x^6y^5} = 2 \cdot \frac{x^7}{x^6} \cdot \frac{y^3}{y^5}$

Step2: Simplify $x$-term (subtract exponents)

$\frac{x^7}{x^6} = x^{7-6} = x^1 = x$

Step3: Simplify $y$-term (subtract exponents)

$\frac{y^3}{y^5} = y^{3-5} = y^{-2} = \frac{1}{y^2}$

Step4: Combine all simplified parts

$2 \cdot x \cdot \frac{1}{y^2}$

Answer:

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