Let's analyze each expression step-by-step and compare them:
1. Expression: [tex]\( \frac{3^3}{3} \)[/tex]
[tex]\[
= 3^{3-1} \quad \text{(Subtract the exponents since the bases are the same)}
= 3^2
\][/tex]
2. Expression: [tex]\( \frac{3^{-3}}{3^4} \)[/tex]
[tex]\[
= 3^{-3-4} \quad \text{(Subtract the exponents)}
= 3^{-7}
\][/tex]
3. Expression: [tex]\( \frac{3^7}{3^0} \)[/tex]
[tex]\[
= 3^{7-0} \quad \text{(Any number to the power of zero is 1, so 3^0 = 1)}
= 3^7
\][/tex]
4. Expression: [tex]\( 3 \times 3^6 \)[/tex]
[tex]\[
= 3^1 \times 3^6 \quad \text{(Since 3 is the same as 3^1)}
= 3^{1+6} \quad \text{(Add the exponents because the bases are the same)}
= 3^7
\][/tex]
5. Expression: [tex]\( 3^3 \times 3^4 \)[/tex]
[tex]\[
= 3^{3+4} \quad \text{(Add the exponents because the bases are the same)}
= 3^7
\][/tex]
Now, comparing each of these simplified forms:
- [tex]\( \frac{3^3}{3} = 3^2 \)[/tex]
- [tex]\( \frac{3^{-3}}{3^4} = 3^{-7} \)[/tex]
- [tex]\( \frac{3^7}{3^0} = 3^7 \)[/tex]
- [tex]\( 3 \times 3^6 = 3^7 \)[/tex]
- [tex]\( 3^3 \times 3^4 = 3^7 \)[/tex]
We observe that all the expressions except for the second one ([tex]\( \frac{3^{-3}}{3^4} \)[/tex]) are equal to [tex]\( 3^7 \)[/tex] or can be simplified to [tex]\( 3^7 \)[/tex].
Thus, the expression that is not equal to the others is the second one: [tex]\( \frac{3^{-3}}{3^4} \)[/tex].
Therefore, the expression that is not equal to the others is:
Option 2: [tex]\( \frac{3^{-3}}{3^4} \)[/tex]
Hence, the expression which is not equal to the others is the second one, or equivalently, the answer is:
### 2
