Fill in the blanks!

Question

-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 simplifying the given expressions:

1. To simplify \( \frac{1}{X^{50}} \), we can express it as \( X^{-50} \). So, the first blank would be X:

   • Simplified: X / X^(50) = X^(-50)

2. We want to get an expression that can subtract with \( 1/r^{4} \). The most straightforward way is to express it as \( r^{-4} \). So, the second blank would be r:

   • 1/r^{4} - 1/r

3. For \( r^{(-4)} - s^{(-1)} \), it appears we already have a form which suggests we may not need to fill anything in, as both terms are negative exponents. So nothing is needed for this one:

   • r^(-4) - s^(-1) (No blanks to fill)

4. In the case of \( \frac{3v^{7}}{u^{12}} \), this can also be expressed as \( 3v^{7}u^{-12} \), matching the form given. So, we confirm:

   • 3v^(7) / u^(12) = 3v^{7}u^{-12} (already given in the last expression)

In summary:

1. First Blank: X
2. Second Blank: r
3. No blanks for the third one.
4. Confirming the fourth one fits without needing any additional input.

Let me know if you have more questions or need further help!