Are 𝑎 to the fourth power and four 𝑎 like terms?
Like terms are terms whose variables and their exponents are the same. 𝑎 to the fourth power and four 𝑎 have the same variable. But four 𝑎 could also be written as four 𝑎 to the first power. So even though these variables are the same, their exponents are different. And that means they’re not like terms.
We can also think about it in another way. What does 𝑎 to the fourth power mean? It means 𝑎 multiplied by itself four times. And what does four 𝑎 mean? That means 𝑎 plus itself four times. And these are not alike.
The answer to the question “Are 𝑎 to the fourth power and four 𝑎 like terms?” is no.