Question

Which of the following is equivalent to the expression below?(attached is the question)

Answer 1

Square roots and exponents

We know that

`\begin{gathered} 36=6^2 \\ \text{and} \\ \sqrt[]{36x^3}=\sqrt[]{36}\cdot\sqrt[]{x^3} \end{gathered}`

Square roots can be expressed as a fraction on the exponent:

`\begin{gathered} \sqrt[]{36x^3}=(36x^3)^{(1)/(2)} \\ \sqrt[]{36}\cdot\sqrt[]{x^3}=\sqrt[]{6^2}\cdot\sqrt[]{x^3} \\ =6^{(2)/(2)}\cdot x^{(3)/(2)} \\ =6x^{(3)/(2)} \end{gathered}`

Answer: C