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: \(\boxed{b^{\frac{11}{12}}}\)