To determine the order of the expressions from least to greatest, let's evaluate each one step-by-step:
1. Expression 1: [tex]\(3^2\)[/tex]
- Calculate: [tex]\(3^2 = 9\)[/tex]
2. Expression 2: [tex]\(2^1 + 3^1\)[/tex]
- First, calculate [tex]\(2^1\)[/tex]: [tex]\(2^1 = 2\)[/tex]
- Then, calculate [tex]\(3^1\)[/tex]: [tex]\(3^1 = 3\)[/tex]
- Add the results together: [tex]\(2 + 3 = 5\)[/tex]
3. Expression 3: [tex]\(2^3 - 2^1\)[/tex]
- First, calculate [tex]\(2^3\)[/tex]: [tex]\(2^3 = 8\)[/tex]
- Then, calculate [tex]\(2^1\)[/tex]: [tex]\(2^1 = 2\)[/tex]
- Subtract the second result from the first: [tex]\(8 - 2 = 6\)[/tex]
Now we have evaluated all expressions:
- [tex]\(3^2 = 9\)[/tex]
- [tex]\(2^1 + 3^1 = 5\)[/tex]
- [tex]\(2^3 - 2^1 = 6\)[/tex]
To order these expressions from least to greatest:
1. [tex]\(2^1 + 3^1 = 5\)[/tex]
2. [tex]\(2^3 - 2^1 = 6\)[/tex]
3. [tex]\(3^2 = 9\)[/tex]
Thus, the order of the expressions from least to greatest is:
[tex]\[
2^1 + 3^1 \quad (5), \quad 2^3 - 2^1 \quad (6), \quad 3^2 \quad (9)
\][/tex]
