+2448 I really don't know how to do these >.<
\(-\sqrt[3]{-54n^7}\)
\(-5\sqrt[4]{128x^4}\)
\(6\sqrt[4]{567x^4}\)
\(4\sqrt[3]{64n^8}\)
+6251 \(-\sqrt[3]{-54n^7} = \\ -((-1)\sqrt[3]{54n^7} = \\ \sqrt[3]{27n^6 \cdot 2n} = \\ 3n^2\sqrt[3]{2n}\)
the rest are similar, give them another try
+6251 The idea is to factor the stuff under the radical into two pieces.
One piece is something that has a clear cube or 4th root and the other piece is the rest.
In the first one we want to break \(-54 n^7\) into pieces one of which we can simply take the cube root of.
\(\left(-3n^2\right)^3 = -27n^6\\ -54n^7 = -27n^6 \cdot 2n \\ \sqrt[3]{-54n^7} = \sqrt[3]{-27n^6 \cdot 2n} = -3n^2 \sqrt[3]{2n} \\ -\sqrt[3]{-54n^7} = -(-3n^2\sqrt[3]{2n}) = 3n^2\sqrt[3]{2n} \)
I'll do one more for you but I'd like to see you work these out yourself
\(-5\sqrt[4]{128x^4} = -5\sqrt[4]{2^7 x^4}=\\ -5\sqrt[4]{2^4 x^4 \cdot 2^3} = -5\cdot 2x\sqrt[4]{2^3} = \\ -10x \sqrt[4]{8}\)
