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2 so I am trying to find what p^4 would be and what q^4 would be.**
Question: If p^2 = 2q^2, how can I solve for p^4 using that same relation?. A: The relationship $p^2=2q^2$ does not determine a specific value of $p$ or $q$. It only represents a relation between these two quantities. In other words, there are infinitely many pairs of $p$ and $q$ that satisfy this equation. Therefore, you cannot solve for $p^4$ based solely on this relationship without additional information about $p$ or $q$.
However, you can express $p^4$ in terms of $q$ based on the given relation. Squaring both sides of the equation $p^2=2q^2$, you get:
$$p^4 = (2q^2)^2$$ $$p^4 = 4q^4$$
So, $p^4$ equals 4 times $q^4$. This means that whatever the value of $q^4$ is, $p^4$ will be four times that value, as long as $p$ and $q$ satisfy the initial relation $p^2=2q^2$.
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