Question

Which expression is equivalent to (x4/3x2/3)1/3

Answer 1

Given

The expression is given in the question

`=(x^{(4)/(3)}*\ x^{(2)/(3)})\ ^{(1)/(3)}`

Find the expression is equivalent to the above expression.

To proof

As expression is given in the question

`=(x^{(4)/(3)}*\ x^{(2)/(3)})\ ^{(1)/(3)}`

By using the properties

product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.

i.e

`x^(a) .x^(b) = x^(a +b)`

Now using this in above

we get

`=x^{(6)/(3)*(1)/(3)}`

Also by using the property

`(x^(a) )^(b) = x^(ab)`

We get
`=x^{(6)/(9)}`

Therefore expression becomes

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

Hence proved