The algebraic expression is given as,
[tex]\sqrt[]{8a^3b^{11}}[/tex]
Consider the following law of exponents,
[tex]\begin{gathered} x^{m+n}=x^m\cdot x^n \\ x^{mn}=(x^m)^n \end{gathered}[/tex]
Note that the variables lie under the square root operator. So the inner expression can be broken down to obtain the most number of terms in squared form,
[tex]\begin{gathered} =\sqrt[]{4\cdot2\cdot a^{2+1}\cdot b^{10+1}} \\ =\sqrt[]{2^2\cdot2\cdot a^2\cdot a\cdot b^{2\cdot5}\cdot b} \\ =\sqrt[]{2^2\cdot2\cdot a^2\cdot a\cdot(b^5)^2^{}\cdot b} \\ =\sqrt[]{2\cdot a\cdot(2ab^5)^2\cdot b} \\ =(2ab^5)\cdot\sqrt[]{2\cdot a\cdot b} \\ =2ab^5\cdot\sqrt[]{2ab} \end{gathered}[/tex]
Thus, the simplified form of the expression is obtained using the law of exponents.
Since the simplified expression is mentioned in option B, it should be the correct choice.
