Question

Fill in the blanks!

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**.