Question

Which of the following is equivalent to the expression below? Select all that apply
`5x (3)/(2)`A)
`\sqrt[3]{(5x) {}^(2) }`B
`5 \sqrt{x ^(3) }`C
`\sqrt{(5x) ^(3) }`D
`5( \sqrt{x) ^(3) }`E
`\sqrt{5x ^(3) }`

Answer 1

5√(x³) and 5(√x)³

Step-by-step explanation:

We will use the following properties:

`\begin{gathered} \sqrt[]{x^a}=x^{(a)/(2)} \\ \sqrt[]{x^a}=(\sqrt[]{x})^a \end{gathered}`

Now, the expression is equivalent to:

`5x^{(3)/(2)}=5\cdot x^{(3)/(2)}=5\cdot\sqrt[]{x^3}`

And it is also equal to:

`5\sqrt[]{x^3}=5(\sqrt[]{x}^{})^3`

Therefore, the equivalent expressions are 5√(x³) and 5(√x)³