Getting answers wrong. Not helpful if the answers are incorrect To convert 5721 to a numeral in base 4, we need to find the largest power of 4 that is less than or equal to 5721.
Let's start by finding the largest power of 4 that is less than or equal to 5721. To do this, we raise 4 to various powers until we find one that is greater than 5721:
\begin{align*}
4^1 &= 4\\
4^2 &= 16\\
4^3 &= 64\\
4^4 &= 256\\
4^5 &= 1024\\
4^6 &= 4096
\end{align*}
We can see that $4^4 = 256$ is the largest power of 4 that is less than 5721.
Next, we divide 5721 by 256 and determine the quotient and remainder:
\[
5721 \div 256 = 22 \text{ remainder } 89
\]
The quotient is 22 and the remainder is 89.
Now, we continue the process with the remainder, 89. We divide 89 by the next lower power of 4, which is $4^3 = 64$:
\[
89 \div 64 = 1 \text{ remainder } 25
\]
The quotient is 1 and the remainder is 25.
Next, we divide 25 by the next lower power of 4, which is $4^2 = 16$:
\[
25 \div 16 = 1 \text{ remainder } 9
\]
The quotient is 1 and the remainder is 9.
Finally, we divide 9 by the smallest power of 4, which is $4^1 = 4$:
\[
9 \div 4 = 2 \text{ remainder } 1
\]
The quotient is 2 and the remainder is 1.
Now, let's combine the remainders in reverse order to get the base 4 numeral:
\[
5721 = 2221_4
\]
Therefore, the numeral representation of 5721 in base 4 is 2221. Answer is incorrect!!!