To simplify the expression:

$\frac{xy}{(7x^{-4})(y^{-2})}$

1. First, simplify the denominator. Use the rule of exponents, $x^a \cdot x^b = x^{a+b}$, and simplify each factor: $(7x^{-4})(y^{-2}) = 7x^{-4}y^{-2}$

2. Now rewrite the original expression: $\frac{xy}{7x^{-4}y^{-2}}$

3. Apply the property of exponents when dividing: $\frac{x^a}{x^b} = x^{a-b}$ and $\frac{y^a}{y^b} = y^{a-b}$: $\frac{xy}{7x^{-4}y^{-2}} = \frac{x^{1 - (-4)}y^{1 - (-2)}}{7} = \frac{x^{5}y^{3}}{7}$

Thus, the simplified expression is:

$\frac{x^5 y^3}{7}$

Would you like any further explanation on the steps?

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Here are 5 follow-up questions for practice:

1. How do you simplify an expression like $\frac{x^2}{x^{-3}}$?
2. What is the rule for dividing terms with the same base in exponents?
3. How do you handle negative exponents when simplifying expressions?
4. What happens to the coefficient when simplifying expressions with variables?
5. Can you explain how to simplify the expression $\frac{a^{-2}b}{5a^{-3}}$?

Tip: Always deal with the coefficients and variables separately when simplifying expressions with multiple factors!