Simplify open parentheses x to the 2 third power close parentheses to the 4 fifths power.

Solution:

Given, open parentheses x to the 2 third power close parentheses to the 4 fifths power.

x to the 2 third power = \(x^\frac{2}{3}\)

Now, x to the 2 third power to the 4 fifths power = \((x^\frac{2}{3})^\frac{4}{5}\)

The expression can be written as \((x^\frac{2}{3})^\frac{4}{5}\)

We know, \((a^{m})^{n}=a^{m\times n}\)

So, \((x^\frac{2}{3})^\frac{4}{5}\) = \(x^{(\frac{2}{3}\times \frac{4}{5})}\)

= \(x^{\frac{(2\times 4)}{(3\times 5)}}\)

= \(x^{\frac{8}{15}}\)

Therefore, the simplified form is \(x^{\frac{8}{15}}\)

Simplify open parentheses x to the 2 third power close parentheses to the 4 fifths power.

Summary:

The simplified form of open parentheses x to the 2 third power close parentheses to the 4 fifths power is \(x^{\frac{8}{15}}\).