Question

Express the following numbers using exponential notations
$(i) 3125$
$(ii) 343$

Answer 1

Hint: Take Least common multiple (LCM) of the given number and write factors in powers. We are first going to find the LCM of the given number, then after we find the LCM, we get the factors of the given number, we write them down on RHS and then if we have like/same factors, we add their power together as they are multiplied together and leave the unlike terms (if present).

Complete step by step solution:
(i)We are going to need the factors of $3125$, so we should find out the LCM of $3125$.

After LCM, we have found out the factors of $3125$. They are
$3125 = 5 \times 5 \times 5 \times 5 \times 5$
We can see that there are like terms in the factors which can be written in terms of power of like terms.
$3125 = {5^5}$
The above form which has been found, is the exponential notation of $3125$.

(ii) We are going to need the factors of $343$, so we should find out the LCM of $343$.

After LCM, we have found out the factors of $343$. They are
$343 = 7 \times 7 \times 7$
We can see that there are like terms in the factors which can be written in terms of power of like terms.
$343 = {7^3}$

The above form which has been found, is the exponential notation of $3125$.

Note: Only when like terms are multiplied together, only then their powers can be added together as we did above to get the exponential notations and if there are not like terms, we can just leave them as it.