Question

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

Answer 1

Answer:

$x^{2/3}$

Step-by-step explanation:

When two terms with the same base are directly next to each other (being multiplied), the powers are added. When a term raised to a power is raised to another power, the powers are multiplied.

Begin by adding (4/3) and (2/3) to get (6/3). Then, multiply (6/3) by (1/3) to get (6/9). This number can be simplified to (2/3).

$(x^{4/3}x^{2/3} )^{1/3} \\\\(x^{6/3})^{1/3}\\\\x^{6/9} = x^{2/3}$

Answer 2

Answer:

$x^{\tfrac 23}$

Step by step explanation:

$\left(x^{\tfrac 43} \cdot x^{\tfrac 23} \right)^{\tfrac 13}\\\\\\=\left(x^{\tfrac 43 + \tfrac 23} \right)^{\tfrac 13}\\\\\\=\left(x^{\tfrac 63} \right)^{\tfrac 13}\\\\\\=\left(x^2 \right)^{\tfrac 13}\\\\\\=x^{\tfrac 23}$