Equivalent expressions SAT question

Choice B is correct. Since $\frac{12}{12}=1$, multiplying the exponent of the given expression by $\frac{12}{12}$ yields an equivalent expression: $a^{(\frac{11}{12})(\frac{12}{12})}=a^{(\frac{132}{144})}$. Since $\frac{132}{144}=132(\frac{1}{144})$, the expression $a^{\frac{132}{144}}$ can be rewritten as $a^{(132)(\frac{1}{144})}$. Applying properties of exponents, this expression can be rewritten as ${(a^{132})}^{\frac{1}{144}}$. An expression of the form ${(m)}^{\frac{1}{k}}$, where $m>0$ and $k>0$, is equivalent to $\sqrt[k]{m}$. Therefore, ${(a^{132})}^{\frac{1}{144}}$ is equivalent to $\sqrt[144]{a^{132}}$.

Choice A is incorrect and may result from conceptual or calculation errors. 

Choice C is incorrect and may result from conceptual or calculation errors. 

Choice D is incorrect and may result from conceptual or calculation errors.