Simplify. Leeve your snswer in redical form.
\[
(7 p)^{\frac{4}{5}}+(7 p)^{\frac{2}{6}}
\]

Step 1 ：Recall that \((a b)^n=a^n b^n\) and \((a^n)^m=a^{n m}\). Therefore, we can simplify each term separately.

Step 2 ：First, simplify \((7 p)^{\frac{4}{5}}\) to get \(7^{\frac{4}{5}} p^{\frac{4}{5}}\).

Step 3 ：Next, simplify \((7 p)^{\frac{2}{6}}\) to get \(7^{\frac{2}{6}} p^{\frac{2}{6}}\).

Step 4 ：However, \(\frac{2}{6}\) can be simplified to \(\frac{1}{3}\), so \(7^{\frac{2}{6}} p^{\frac{2}{6}}\) can be further simplified to \(7^{\frac{1}{3}} p^{\frac{1}{3}}\).

Step 5 ：Finally, add the two simplified terms together to get \(7^{\frac{4}{5}} p^{\frac{4}{5}} + 7^{\frac{1}{3}} p^{\frac{1}{3}}\).

Step 6 ：Thus, the simplified form of the given expression is \(\boxed{7^{\frac{4}{5}} p^{\frac{4}{5}} + 7^{\frac{1}{3}} p^{\frac{1}{3}}}\).