To solve these equations, we perform the operations step-by-step.
1. [tex]\( 7 \cdot 7 \cdot 7 \cdot 7 \)[/tex]
- We multiply the number 7 four times.
- [tex]\( 7 \cdot 7 = 49 \)[/tex]
- [tex]\( 49 \cdot 7 = 343 \)[/tex]
- [tex]\( 343 \cdot 7 = 2401 \)[/tex]
So, [tex]\( 7 \cdot 7 \cdot 7 \cdot 7 = 2401 \)[/tex].
2. [tex]\( 7 + 7 + 7 + 7 \)[/tex]
- We add the number 7 four times.
- [tex]\( 7 + 7 = 14 \)[/tex]
- [tex]\( 14 + 7 = 21 \)[/tex]
- [tex]\( 21 + 7 = 28 \)[/tex]
So, [tex]\( 7 + 7 + 7 + 7 = 28 \)[/tex].
3. [tex]\( 7 + 7 + 7 - 7 \)[/tex]
- We perform the addition and subtraction in order.
- [tex]\( 7 + 7 = 14 \)[/tex]
- [tex]\( 14 + 7 = 21 \)[/tex]
- [tex]\( 21 - 7 = 14 \)[/tex]
So, [tex]\( 7 + 7 + 7 - 7 = 14 \)[/tex].
4. [tex]\( 7 + 7 + 7 \div 7 \)[/tex]
- We follow the order of operations, performing the division first and then the additions.
- [tex]\( 7 \div 7 = 1 \)[/tex]
- [tex]\( 7 + 7 = 14 \)[/tex]
- [tex]\( 14 + 1 = 15 \)[/tex]
So, [tex]\( 7 + 7 + 7 \div 7 = 15 \)[/tex].
5. [tex]\( 7 \cdot 7 - 7 \cdot 7 \)[/tex]
- We perform the multiplications first and then the subtraction.
- [tex]\( 7 \cdot 7 = 49 \)[/tex]
- [tex]\( 7 \cdot 7 = 49 \)[/tex]
- [tex]\( 49 - 49 = 0 \)[/tex]
So, [tex]\( 7 \cdot 7 - 7 \cdot 7 = 0 \)[/tex].
6. [tex]\( 7 - 7 + 7 \cdot 7 \)[/tex]
- We follow the order of operations, performing the multiplication first and then the additions and subtractions.
- [tex]\( 7 \cdot 7 = 49 \)[/tex]
- [tex]\( 7 - 7 = 0 \)[/tex]
- [tex]\( 0 + 49 = 49 \)[/tex]
So, [tex]\( 7 - 7 + 7 \cdot 7 = 49 \)[/tex].
Therefore, the results for the given equations are:
[tex]\( (2401, 28, 14, 15.0, 0, 49) \)[/tex].
