Answer :
Let's analyze and compare the given mathematical expressions step by step to determine which one is not equivalent to the others.
1. Expression: \(3 + 3 + 3 + 3\)
[tex]\[ 3 + 3 + 3 + 3 = 12 \][/tex]
2. Expression: \(3^4\)
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
3. Expression: \(3^2 \times 3^2\)
[tex]\[ 3^2 = 9 \][/tex]
[tex]\[ 9 \times 9 = 81 \][/tex]
4. Expression: \(3 \times 3 \times 3 \times 3\)
[tex]\[ 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Now, let's list the results clearly:
- \(3 + 3 + 3 + 3 = 12\)
- \(3^4 = 81\)
- \(3^2 \times 3^2 = 81\)
- \(3 \times 3 \times 3 \times 3 = 81\)
From these calculations, it is evident that three of the expressions yield the value 81, while one of them yields 12. Therefore, the expression that is not equivalent to the others is:
[tex]\[ 3 + 3 + 3 + 3 = 12 \][/tex]
1. Expression: \(3 + 3 + 3 + 3\)
[tex]\[ 3 + 3 + 3 + 3 = 12 \][/tex]
2. Expression: \(3^4\)
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]
3. Expression: \(3^2 \times 3^2\)
[tex]\[ 3^2 = 9 \][/tex]
[tex]\[ 9 \times 9 = 81 \][/tex]
4. Expression: \(3 \times 3 \times 3 \times 3\)
[tex]\[ 3 \times 3 \times 3 \times 3 = 81 \][/tex]
Now, let's list the results clearly:
- \(3 + 3 + 3 + 3 = 12\)
- \(3^4 = 81\)
- \(3^2 \times 3^2 = 81\)
- \(3 \times 3 \times 3 \times 3 = 81\)
From these calculations, it is evident that three of the expressions yield the value 81, while one of them yields 12. Therefore, the expression that is not equivalent to the others is:
[tex]\[ 3 + 3 + 3 + 3 = 12 \][/tex]
