Question

Can anybody help me solve this pleaseeeeeee!!!!!!! I know you see this

Answer 1

The algebraic expression is given as,

`\sqrt[]{8a^3b^(11)}`

Consider the following law of exponents,

`\begin{gathered} x^(m+n)=x^m\cdot x^n \\ x^(mn)=(x^m)^n \end{gathered}`

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,

`\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}`

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.