Simplify open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power.

Solution:

We have to simplify open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power.

x to the 2 fifths power = \(x^{\frac{2}{5}}\)

Open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power can be written as

\((x^{\frac{2}{5}})^{\frac{5}{6}}\)

Using the law of exponents:

\((x^{m})^{n}=x^{(m\times n)}\)

So, \((x^{\frac{2}{5}})^{\frac{5}{6}}\) becomes \(x^{(\frac{2}{5}\times \frac{5}{6})}\)

On simplification,

= \(x^{\frac{10}{30}}\)

= \(x^{\frac{1}{3}}\)

Therefore, by simplifying we get \(x^{\frac{1}{3}}\).

Simplify open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power.

Summary:

On simplifying open parenthesis x to the 2 fifths power close parentheses to the 5 sixths power is \(x^{\frac{1}{3}}\).