[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{a}{b^{3} }\right)^{4} \end{gathered}$}[/tex]
Use the rules of exponents to simplify the expression.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{a^{1} }{b^{3}}\right)^{4} \end{gathered}$}[/tex]
To raise the quotient of two numbers to a power, raise each power to the power and then divide it.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{(a^{1})^{4} }{(b^{3})^{4} } \end{gathered}$}[/tex]
To raise a power to another power, multiply the exponents.
- [tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{a^{4} }{b^{3\times4} } \end{gathered}$}[/tex]
Multiply 3 by 4.
- [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{a^{4} }{b^{12} } \end{gathered}$}}[/tex]
We conclude that: the correct option is "B".
