The problem provided asks to simplify the expression $\frac{7x^5}{3x^{-2}y^3}$ such that all exponents are positive.

Let's simplify the expression step-by-step:

1. Rewrite the expression with positive exponents: To do this, we'll move the term with a negative exponent from the denominator to the numerator.

   The expression is: $\frac{7x^5}{3x^{-2}y^3}$

2. Apply the exponent rule: When a term with a negative exponent is moved to the opposite part of a fraction (from numerator to denominator or vice versa), the sign of the exponent changes. Thus, $x^{-2}$ in the denominator can be moved to the numerator as $x^2$.

   So, the expression becomes: $\frac{7x^5 \cdot x^2}{3y^3}$

3. Combine like terms: In the numerator, combine the $x$-terms by adding their exponents: $x^5 \cdot x^2 = x^{5+2} = x^7$

   Now the expression is: $\frac{7x^7}{3y^3}$

4. Final simplified expression: Since all exponents are positive, this is the simplified form of the expression: $\frac{7x^7}{3y^3}$

This expression has all positive exponents, and it is now fully simplified.

Would you like more details on any of the steps, or do you have any additional questions?

Related Questions:

1. How do you handle negative exponents in the numerator?
2. What is the rule for multiplying terms with the same base?
3. How do you simplify expressions involving variables with different bases?
4. Can you provide more examples of simplifying fractions with negative exponents?
5. How do exponent rules apply when dividing powers with the same base?

Tip:

Remember, when simplifying expressions with exponents, always aim to express the final answer with positive exponents unless otherwise specified.