Question

Which of the following are equivalent to the expression x1/2 • x1/3 select all that apply

Answer 1

Answer: The answer is (2), (4) and (6).

Step-by-step explanation: The given expression is

`E=x^(1)/(2)* x^(1)/(3).`

We are to select all the correct options from the given expressions that are equivalent to the above expression.

We have

`E\\\\=x^(1)/(2)* x^(1)/(3)\\\\=x^{(1)/(2)+(1)/(3)}\\\\=x^(3+2)/(6)\\\\=x^(5)/(6)\\\\=\sqrt[6]{5}.`

Thus, the correct options are

(2)
`x^{(1)/(2)+(1)/(3)},`

(4)
`x^(5)/(6),`

(6)
`\sqrt[6]{5}.`

Answer 2

`x^{(1)/(2)+(1)/(3) }`,
`x^{(5)/(6) }` and
`\sqrt[6]{x^(5) }`

Explanation:

`a^(m) a^(n) =a^(m+n)`

So,
`x^{(1)/(2) } x^{(1)/(3) } =x^{(1)/(2) +(1)/(3) }`

Also,

`x^{(1)/(2) +(1)/(3) } =x^{(3+2)/(6) } =x^{(5)/(6) }`

`x^{(5)/(6) } =(x^(5) )^{(1)/(6) }= \sqrt[6]{x^(5) }`