Question

Fill in the blanks!
• Simplified - _ / X^(50)
• _ - x^(-50)

1/r^(4) - 1/_

r^(-4) - s^(-1)

3v^(7) / u^(12)

3v^(7)u^(-12)

Answer 1

Let's fill in the blanks based on the patterns observed in the equations you provided:

1. Simplified - **X^(50) / X^(50)**
- This is the simplification where an expression is divided by itself, resulting in 1.

2. **x^(50)** - **x^(-50)**
- This requires an equivalent positive exponent result. This can be written as:
**x^(50) = 1 / x^(-50)**.

3. 1/r^(4) - 1/**r^(4)**
- This keeps the same form, where both terms are fractions over the same base.

4. r^(-4) - s^(-1)
- Given the format of the first term, let's say the second should have a similar base result. So we could articulate this as:
- **r^(-4)** - **r^(-4)**, making sense of the formatting as both terms are compatible.

5. 3v^(7) / u^(12)
- This term represents a rational expression already simplified.

6. 3v^(7)u^(-12)
- This is the same term reorganized into a single fraction, represented with a negative exponent to indicate inversion.

Here’s the complete filling in of the blanks:

- Simplified - X^(50) / X^(50)
- X^(50) - X^(-50)
- 1/r^(4) - 1/r^(4)
- r^(-4) - r^(-4)
- 3v^(7) / u^(12)
- 3v^(7)u^(-12)

Feel free to specify if you would like different values or terms!