Question

Match each expression with a fractional exponent to an equivalent radical expression. Select the correct letter.

Answer 1

To convert from the fractional exponent form to the radical form, we can use the following:

`a^{(b)/(c)}=(\sqrt[c]{a}^{})^b`

Thus, let's apply for each:

`x^{(1)/(2)}=(\sqrt[2]{x})^1=\sqrt[]{x}\to B`
`x^{(1)/(3)}=(\sqrt[3]{x})^1=\sqrt[3]{x}\to D`
`x^{(2)/(3)}=(\sqrt[3]{x})^2\to C`
`x^{(3)/(2)}=(\sqrt[2]{x})^3=(\sqrt[]{x})^3\to A`