Question

How do you write each number as a power of the given base: \[49\], base \[7\]?

Answer 1

Hint: From the question given we have been asked to write the given number as a power of the given base. Here the given number is $49$ and the required base is $7$ . So, we will multiply it with itself multiple times until we get the required number starting from $0$ times.

Complete step by step answer:
From the question given we have been asked to write the number \[49\] as a power of a number with base \[7\].
We can clearly understand that the base number should be \[7\].
We have to find out, to which power of the base number \[7\] does the given number \[49\] will be equal.
Now, we have to find out the values of powers of the given base number \[7\].
First of all, let us find out the ${{0}^{th}}$ power of \[7\].
So, now we have to find out the value of \[{{7}^{0}}\].
We know that ${{0}^{th}}$ power of any number will be equal to one.
Therefore, \[{{7}^{0}}=1\]
So, now we have to find out the first power of \[7\].
So, now we have to find out the value of \[{{7}^{1}}\]
We know any number to the power one will be equal to the number itself.
Therefore, \[{{7}^{1}}=7\]
So, now we have to find out the second power of \[7\].
So, now we have to find out the value of \[{{7}^{2}}\].
\[\Rightarrow {{7}^{2}}=7\times 7\]
\[\Rightarrow {{7}^{2}}=49\]
Therefore the number \[49\] can be written as \[{{7}^{2}}\] that is the second power of the base number \[7\] .

Note: We should be well known about the powers and bases of a number. Also, we should be well known about finding the power of a given number and base of a given number. Also, we should know how to write the given number into the power of a number. Also, we should be careful while doing the calculation. Similarly we can express $343$ as ${{7}^{3}}$ .