To write the equation \(\frac{2}{3} a + 5 a^3 + 4 a^4 - 2 a^5\) in standard form, we need to arrange the terms in descending order of their powers.
Here's the given expression:
[tex]\[ \frac{2}{3} a + 5 a^3 + 4 a^4 - 2 a^5 \][/tex]
Now let's list the terms in order of descending powers of \(a\):
- The highest power of \(a\) is \(a^5\) with coefficient \(-2\), so we start with \(-2 a^5\).
- Next is \(a^4\) with coefficient \(4\), which gives us \(4 a^4\).
- Following that, we have \(a^3\) with coefficient \(5\), resulting in \(5 a^3\).
- Finally, we have \(a\) with the fractional coefficient \(\frac{2}{3}\), which remains as \(\frac{2}{3} a\).
Combining these, the standard form of the equation is:
[tex]\[ -2 a^5 + 4 a^4 + 5 a^3 + \frac{2}{3} a \][/tex]
Therefore, the correct option is:
A. \(-2 a^5 + 4 a^4 + 5 a^3 + \frac{2}{3} a\)
This matches option A, so the correct answer is [tex]\( \boxed{A} \)[/tex].
