Let $a,$ $b,$ and $c$ be positive real numbers such that $a + b^2 + c^3 = \frac{325}{9}.$  Find the minimum value of
\[a^2 + b^3 + c^4.\]
Question:
Let $a,$ $b,$ and $c$ be positive real numbers such that $a + b^2 + c^3 = \frac{325}{9}.$  Find the minimum value of
\[a^2 + b^3 + c^4.\]
Answer:
Let's think step by step.

user
\frac{2807}{27}
Let $a,$ $b,$ and $c$ be positive real numbers such that $a + b^2 + c^3 = \frac{325}{9}.$  Find the minimum value of
\[a^2 + b^3 + c^4.\]
train