Question

Which expression is equivalent to (x^4/3 x^2/3)^1/3

O x^2/3
O x^2/9
O
x^8/27
O x^7/3

Answer 1

We conclude that:

`\left(\:\:(x^4)/((3x^2)/(3))\right)^{(1)/(3)}\:=\:x^{(2)/(3)}`

Hence, option A i.e.
`x^{(2)/(3)}` is true.

Explanation:

Given the expression

`\left(\:\:(x^4)/((3x^2)/(3))\right)^{(1)/(3)}`

Apply exponent rule:
`\left((a)/(b)\right)^c=(a^c)/(b^c)`

`\left((x^4)/((3x^2)/(3))\right)^{(1)/(3)}=\frac{\left(x^4\right)^{(1)/(3)}}{\left((3x^2)/(3)\right)^{(1)/(3)}}`

`=\frac{x^{(4)/(3)}}{\left((3x^2)/(3)\right)^{(1)/(3)}}` ∵
`\:\:\:\left(x^4\right)^{(1)/(3)}=x^{(4)/(3)}`

`=\frac{x^{(4)/(3)}}{\frac{\left(3x^2\right)^{(1)/(3)}}{3^{(1)/(3)}}}`

`=\frac{x^{(4)/(3)}}{x^{(2)/(3)}}`

Apply exponent rule:
`(x^a)/(x^b)=x^(a-b)`

`=x^{(4)/(3)-(2)/(3)}`

`=x^{(2)/(3)}\\`

Therefore, we conclude that:

`\left(\:\:(x^4)/((3x^2)/(3))\right)^{(1)/(3)}\:=\:x^{(2)/(3)}`

Hence, option A i.e.
`x^{(2)/(3)}` is true.