Radicals
Rational exponents: Products and quotients with negative exponents
Simplify the expression.
\[
\frac{b^{\frac{3}{2}} b^{-\frac{1}{4}}}{b^{\frac{1}{3}}}
\]

Write your answer using only positive exponents. Assume that all variables are positive real numbers.

Step 1 ：Combine the exponents by adding them when multiplying: \( b^{\frac{3}{2}} \cdot b^{-\frac{1}{4}} = b^{\frac{3}{2} - \frac{1}{4}} \)

Step 2 ：Simplify the exponent: \( b^{\frac{3}{2} - \frac{1}{4}} = b^{\frac{6}{4} - \frac{1}{4}} = b^{\frac{5}{4}} \)

Step 3 ：Subtract the exponent in the denominator from the exponent in the numerator: \( \frac{b^{\frac{5}{4}}}{b^{\frac{1}{3}}} = b^{\frac{5}{4} - \frac{1}{3}} \)

Step 4 ：Find a common denominator for the exponents: \( b^{\frac{5}{4} - \frac{1}{3}} = b^{\frac{15}{12} - \frac{4}{12}} \)

Step 5 ：Simplify the exponent: \( b^{\frac{15}{12} - \frac{4}{12}} = b^{\frac{11}{12}} \)

Step 6 ：Write the final answer with only positive exponents: \(\boxed{b^{\frac{11}{12}}}\)