Question

Express using a radical (picture provided)

Answer 1

C

Explanation:

First note that

`(1)/(3)=(5)/(15)\Rightarrow x^{(1)/(3)}=x^{(5)/(15)};\\ \\\\(1)/(5)=(3)/(15)\Rightarrow y^{(1)/(5)}=y^{(3)/(15)}`

Now use the property

`a^n\cdot b^n=(ab)^n,`

so

`x^{(5)/(15)}\cdot y^{(3)/(15)}=(x^5)^{(1)/(15)}\cdot (y^3)^{(1)/(15)}=(x^5y^3)^{(1)/(15)}.`

Since
`a^{(1)/(15)}=\sqrt[15]{a},`

you have

`15(x^5y^3)^{(1)/(15)}=15\sqrt[15]{x^5y^3} .`