What are the intermediate steps in changing $(25-3\sqrt{69})^{1/3}$ to $\frac{2^{2/3}}{(25+3\sqrt{69})^{1/3}} $?

Question

I was messing with WolframAlpha trying to simplify a function, and I noticed that $$(25-3\sqrt{69})^{1/3}$$ somehow has the alternate form of: $$ \frac{2^{2/3}}{(25+3\sqrt{69})^{1/3}} $$

I tried manipulating it on my own with my calculus-level education, but I couldn't figure out where that 2 came from or how a sign change within the radical can occur in like this.

Here's the link to WolframAlpha showing what my input was; any guidance in this problem would be very appreciated!

Answer 1

They've just multiplied and divided by $(25+3\sqrt{69})^{1/3}$.

So, $(25-3\sqrt{69})^{1/3}\cdot(25+3\sqrt{69})^{1/3} = (625 - 9(69))^{1/3} = 4^{1/3} = 2^{2/3}$