Question

Convert 343 as a power of 7

Answer 1

Hint: Here, we have to use the concept of the factorization. Factorization is the process in which a number is written in the forms of its small factors which on multiplication give the original number. We will factorize the given number and then we will write it in the exponent form.

Complete step-by-step answer:
Given number is 343.
Now we will factorize the given number into its small factors.
Factors are the smallest numbers with which the given number is divisible and their multiplication will give the original number.
Therefore, the number 343 in terms of its factors is written as
\[343 = 7 \times 7 \times 7\]
Now we will write it in the exponent form or power form. An exponent shows how many times a number is being multiplied to itself. In our case it is three as number 7 is being multiplied with itself three times. Therefore, we get
\[ \Rightarrow 343 = {7^3}\]
Hence, 343 is equal to \[{7^3}\] or we can write it as 7 raised to the power 3.

Note: Here we found out the exponent of 7 is 3, therefore we can say 343 is the cube of 7. A Cube of a number is defined as the number which is being multiplied by itself three times. We should not get confused between cubes with the square. The square of a number is defined as the number which is being multiplied by itself two times.
Square of a number \[ = {a^2}\]
Cube of a number \[ = {a^3}\]
We generally pronounce it as a number raised to the power two or three according to the condition.