Question

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

Answer 1

Given

The expression is given in the question

$=(x^{\frac{4}{3}}\times\ x^{\frac{2}{3}})\ ^{\frac{1}{3}}$

Find the expression is equivalent to the above expression.

To proof

As expression is given in the question

$=(x^{\frac{4}{3}}\times\ x^{\frac{2}{3}})\ ^{\frac{1}{3}}$

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

$=x^{\frac{6}{3}\times\frac{1}{3}}$

Also by using the property

$(x^{a} )^{b} = x^{ab}$

We get$=x^{\frac{6}{9}}$

Therefore expression becomes

$= x^{\frac{2}{3}}$

Hence proved