Question

The following work models how to write the quotient…see photo

Answer 1

`\sqrt[6]{2}`

Explanation:

You want the expression 2^(2/3)/2^(1/2) in simplest radical form.

Quotient property of exponents

The quotient property tells you ...

(a^b)/(a^c) = a^(b-c)

Fractional exponents

The relation between fractional exponents and roots is ...

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

Application

`(2^(2)/(3))/(2^(1)/(2))=2^{(2)/(3)-(1)/(2)}=2^(1)/(6)=\boxed{\sqrt[6]{2}}`