Certainly! Let's solve the equation step by step:
1. We start with the given equation:
[tex]\[
6 + \sqrt[4]{m} = 8
\][/tex]
2. To isolate the term involving [tex]\( m \)[/tex], we subtract 6 from both sides of the equation:
[tex]\[
\sqrt[4]{m} = 8 - 6
\][/tex]
Simplifying the right-hand side, we get:
[tex]\[
\sqrt[4]{m} = 2
\][/tex]
3. Next, we need to eliminate the fourth root by raising both sides of the equation to the power of 4:
[tex]\[
(\sqrt[4]{m})^4 = 2^4
\][/tex]
On the left-hand side, raising the fourth root of [tex]\( m \)[/tex] to the power of 4 simply leaves us with [tex]\( m \)[/tex]:
[tex]\[
m = 2^4
\][/tex]
4. Now calculate [tex]\( 2^4 \)[/tex]:
[tex]\[
2^4 = 16
\][/tex]
Therefore, the solution to the equation is:
[tex]\[
m = 16
\][/tex]
So the correct answer is:
a. [tex]\(\{16\}\)[/tex]
