What is the meaning of this question? Exercise: Consider the question of representing integers with the base $a$ . In order to name the integers in this system we need words for the digits $0$, $1, \ldots, a –1$ and for the various powers of $a$: $a$, $a^2$, $a^3, \ldots$. How many different number words are needed to name all numbers from zero to one thousand, for $a = 2$, $3$, $4$, $5,\ldots, 15$? Which base requires the fewest? (Examples: If $a = 10$, we need ten words for the digits, plus words for $10$, $100$, and $1000$, making a total of $13$. For $a = 20$, we need twenty words for the digits, plus words for $20$ and $400$, making a total of $22$. If $a = 100$, we need $100 + 1$.)

PS : I don't need solution , I just need a brief explanation on what this question is asking about as my English is not that good enough to understand it
It's the number of words we need to define the number system with a specific base. Since an integer with base $a$ is represented by $x_1\times1+x_2\times a+x_3\times a^2$ and so on. We need words to represent $x_1$,$x_2$,$x_3$... Those are the symbols from $0$,$1$,$2 \ldots,a-1$ that is a number of words and also the words for the powers of $a$ since the basic set of symbols with value below a is being multiplied by the powers of $a$. Also there is a constraint here, numbers up to only, so the limit and the question of which uses least number of words. But in case of absence of constraints, it would be infinite number of words in each case.
It's the number of words we need to define the number system with a specific base. Since an integer with base $a$ is represented by $x_1\times1+x_2\times a+x_3\times a^2$ and so on. We need words to represent $x_1$,$x_2$,$x_3$... Those are the symbols from $0$,$1$,$2 \ldots,a-1$ that is a number of words and also the words for the powers of $a$ since the basic set of symbols with value below a is being multiplied by the powers of $a$. Also there is a constraint here, numbers up to only, so the limit and the question of which uses least number of words. But in case of absence of constraints, it would be infinite number of words in each case.