Simplify open parentheses x to the 2 ninths power close parentheses to the 3 eighths power.

Solution:

Given, open parenthesis x to the 2 ninths power close parentheses to the 3 eighths power.

x to the 2 ninths power = \((x)^{\frac{2}{9}}\)

open parenthesis x to the 2 ninths power close parentheses to the 3 eighths power = \((x^{\frac{2}{9}})^{\frac{3}{8}}\)

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

So, \((x\frac{2}{9})\frac{3}{8}\) = \(x^{(\frac{2}{9}\times \frac{3}{8})}\)

= \(x^{\frac{(2\times 3)}{(9\times 8)}}\)

= \(x^{\frac{(6)}{(72)}}\)

= \(x^{\frac{1}{12}}\)

Therefore, the simplified form is \(x^{\frac{1}{12}}\).

Simplify open parentheses x to the 2 ninths power close parentheses to the 3 eighths power.

Summary:

The simplified form of open parenthesis x to the 2 ninths power close parentheses to the 3 eighths power is  \(x^{\frac{1}{12}}\).