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

Explanation:

Step1: Simplify the coefficient

Divide 14 by 21. $\frac{14}{21}=\frac{2}{3}$.

Step2: Use exponent - subtraction rule for $x$ terms

For $x$ terms, use the rule $\frac{x^m}{x^n}=x^{m - n}$. Here $m = 3$ and $n = 6$, so $\frac{x^{3}}{x^{6}}=x^{3-6}=x^{-3}=\frac{1}{x^{3}}$.

Step3: Use exponent - subtraction rule for $y$ terms

For $y$ terms, with $m = 7$ and $n = 6$, $\frac{y^{7}}{y^{6}}=y^{7 - 6}=y^{1}=y$.

Step4: Combine the results

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

Answer:

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