Fill in the blanks!

Question

Simplify these expressions that have a variable base.
y^(-6)
=1/y^(_)

p^(0) = _
p=/ 0

u^(-12)-r^(-5)
= 1/u^(_) - 1/r^(_)

Answer 1

Let's fill in the blanks for each expression:

1. For \( y^{-6} \): \[ y^{-6} = \frac{1}{y^{6}} \] So, the first blank is 6.

2. For \( p^{0} \): \[ p^{0} = 1 \quad \text{(as long as } p \neq 0\text{)} \] The blank here is 1.

3. For \( u^{-12} - r^{-5} \): \[ u^{-12} = \frac{1}{u^{12}} \quad \text{and} \quad r^{-5} = \frac{1}{r^{5}} \] Thus: \[ u^{-12} - r^{-5} = \frac{1}{u^{12}} - \frac{1}{r^{5}} \] Using the same format as given, we can rewrite it as: \[ \frac{1}{u^{12}} - \frac{1}{r^{5}} \] So, the blanks are 12 and 5 respectively.

Putting it all together:

1. \( y^{-6} = \frac{1}{y^{6}} \)
2. \( p^{0} = 1 \) (where \( p \neq 0 \))
3. \( u^{-12} - r^{-5} = \frac{1}{u^{12}} - \frac{1}{r^{5}} \)

Thus, the final answers are:

• 6
• 1
• 12 and 5.