Answer:
D.
[tex]\frac{ {b}^{ \frac{7}{12} } }{ {b}^{2} } [/tex]
Step-by-step explanation:
[tex] \frac{ {b}^{ - \frac{7}{4}} \times b }{ ({ {b}^{ - \frac{1}{2} } )}^{ - \frac{4}{3} } } [/tex]
Applying Multiplication power and Power law of exponentials
[tex] = \frac{ {b}^{1 - \frac{7}{4} } }{ {b}^{ - \frac{1}{2} \times - \frac{4}{3} } } [/tex]
[tex] = \frac{ {b}^{ - \frac{3}{4} } }{ {b}^{ \frac{2}{3} } } [/tex]
Applying Division law of exponentials
[tex] = {b}^{ - \frac{3}{4} - \frac{2}{3} } [/tex]
[tex] = {b}^{ - \frac{17}{12} } [/tex]
[tex] = \frac{ {b}^{ \frac{7}{12} } }{ {b}^{2} } [/tex]