Question

fully simplify using only positive exponents.\\(\frac{14x^{3}y^{7}}{21x^{6}y^{6}}\\)

Explanation:

Step1: Simplify the constant coefficients

$\frac{14}{21} = \frac{2}{3}$

Step2: Simplify $x$-terms using exponent rule

$\frac{x^3}{x^6} = x^{3-6} = x^{-3} = \frac{1}{x^3}$

Step3: Simplify $y$-terms using exponent rule

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

Step4: Combine all simplified parts

$\frac{2}{3} \cdot \frac{1}{x^3} \cdot y$

Answer:

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