To fully simplify the expression $7x^5y^5 \cdot \left(14x^4y^2\right)$, let's follow the steps:

1. Simplify the constants: $7 \cdot 14 = 98$

2. Multiply the $x$ terms: $x^5 \cdot x^4 = x^{5+4} = x^9$

3. Multiply the $y$ terms: $y^5 \cdot y^2 = y^{5+2} = y^7$

Putting it all together, the simplified expression is:

$98x^9y^7$

Would you like more details on this process or have any other questions? Here are some related questions you might find interesting:

1. How do you simplify expressions involving more than two terms?
2. What are the rules for multiplying exponents with the same base?
3. How does one factor polynomials involving multiple variables?
4. Can you explain the distributive property with variables?
5. What happens when dividing similar expressions?

Tip: Always simplify the coefficients and like bases separately before combining them in expressions.