In the following question , which mathematical operators can be used so that the expression will become correct ?
`8**5**27**3**16`

Options

A. `xx,=,-,-:`
B. `+,-:,=,-`
C. `xx,=,-+`
D. `+,xx,-,=`

Answer

To solve the expression `8 ** 5 ** 27 ** 3 ** 16` and determine which mathematical operators can be used to make the expression correct, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The expression is `8 star 5 star 27 star 3 star 16`. We need to replace the `star` with mathematical operators such that the equation holds true.

2. **Using the Board Mass Rule**:
We will follow the order of operations (BODMAS/BIDMAS):
- B: Brackets
- O: Orders (i.e., powers and square roots, etc.)
- D: Division
- M: Multiplication
- A: Addition
- S: Subtraction

3. **Evaluating Each Option**:
We will evaluate the four options provided to see which one makes the equation true.

**Option 1**: `8 * 5 = 27 - 3 / 16`
- Calculate left side: `8 * 5 = 40`
- Calculate right side: `27 - (3 / 16)` is not equal to 40.
- **Conclusion**: This option is incorrect.

**Option 2**: `8 + 5 / 27 = 3 - 16`
- Calculate left side: `8 + (5 / 27)` is a fraction and does not equal `-13`.
- **Conclusion**: This option is incorrect.

**Option 3**: `8 * 5 = 27 - 3 * 16`
- Calculate left side: `8 * 5 = 40`
- Calculate right side: `27 - (3 * 16) = 27 - 48 = -21`, which is not equal to 40.
- **Conclusion**: This option is incorrect.

**Option 4**: `8 + 5 * 27 - 3 = 16`
- Calculate left side:
- First, do the multiplication: `5 * 27 = 135`
- Then, do the addition and subtraction: `8 + 135 - 3 = 140`
- This does not equal 16.
- **Conclusion**: This option is incorrect.

4. **Final Conclusion**:
After evaluating all options, it appears that none of the options provided make the expression correct. However, based on the video transcript, it seems that the third option was considered correct, but it was incorrectly evaluated.