Final answer:
The simplified expression with positive rational exponents is a^(21/7) / b * c. We achieved this by subtracting the exponents of like bases in the denominator from those in the numerator and ensuring all resulting exponents are positive.
Step-by-step explanation:
To simplify the expression (a^(4/7)b^(-2/7)c^(5/8))/(a^(-17/7)b^(5/7)c^(-3/8)) using positive rational exponents, we use the properties of exponents to combine the like bases by subtracting the exponents of corresponding bases in the denominator from those in the numerator.
For the base a, we have a^(4/7) / a^(-17/7), which simplifies to a^((4/7)-(-17/7)) = a^(21/7).
For the base b, we have b^(-2/7) / b^(5/7), which simplifies to b^((-2/7)-(5/7)) = b^(-7/7) = b^(-1), but since we want only positive exponents, we can write b^(-1) as 1/b.
For the base c, we have c^(5/8) / c^(-3/8), which simplifies to c^((5/8)-(-3/8)) = c^(8/8) = c^1 = c.
Combining these results, we get the simplified expression a^(21/7) / b * c. This expression has only positive rational exponents, as required.