Final answer:
To simplify ((2a^5b^4)/(8b^2))^3 with positive exponents, divide the numerator and denominator separately. Simplify the numerator and denominator by dividing by their greatest common factor. Cube both the numerator and denominator. The simplified expression is (1/64)(a^15/b^6).
Step-by-step explanation:
To simplify ((2a^5b^4)/(8b^2))^3 with positive exponents, we can start by simplifying the numerator and denominator separately.
The numerator, 2a^5b^4, has both the variable terms a^5 and b^4. The denominator, 8b^2, only has the variable term b^2. Therefore, we can simplify the expression as:
((2a^5b^4)/(8b^2))^3 = ((2/8)(a^5/b^2))^3
Next, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2. This gives us:
((2/8)(a^5/b^2))^3 = ((1/4)(a^5/b^2))^3
Finally, we can cube both the numerator and the denominator, which gives us the simplified expression:
((1/4)(a^5/b^2))^3 = (1/64)(a^15/b^6)