Final Answer:
The expression (u⁻⁸)/(v⁻³) with only positive exponents is (v³)/(u⁸).
Step-by-step explanation:
To rewrite the expression (u⁻⁸)/(v⁻³) with positive exponents, we'll apply the reciprocal rule of exponents. When a term with a negative exponent is moved to the denominator, it becomes positive. Therefore, by relocating u⁻⁸ to the denominator and v⁻³ to the numerator, the expression transforms to (v³)/(u⁸).
Initially, (u⁻⁸)/(v⁻³) represents u raised to the power of -8 divided by v raised to the power of -3. Using the reciprocal rule, u⁻⁸ is moved to the denominator, becoming u⁸, and v⁻³ is moved to the numerator, becoming v³. Therefore, the final expression with positive exponents becomes (v³)/(u⁸).
This transformation to positive exponents simplifies the expression, making it easier to work with or incorporate into other mathematical operations, calculations, or equations. The new form (v³)/(u⁸) provides a clearer representation without negative exponents, aiding in further analysis or manipulation within various mathematical contexts.