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Question

𝑦
0
=
y
0
=

−
(
𝑦
)
0
=
−(y)
0
=

0
0
=
0
0
=

(
−
5
)
0
=
(−5)
0
=

(
𝑦
⋅
−
5
)
0
=
(y⋅−5)
0=

Answer 1

To fill in the blanks using the rules of exponents, we will use the fact that any non-zero number raised to the power of 0 is 1, and that the 0th power of 0 is typically considered undefined.

1. \( y^0 = 1 \) (assuming \( y \neq 0 \))
2. \( - (y^0) = - 1 \) (again, assuming \( y \neq 0 \))
3. \( 0^0 = \text{undefined} \) (sometimes defined as 1 in combinatorics, but generally considered undefined in other contexts)
4. \( (-5)^0 = 1 \)
5. \( (y \cdot -5)^0 = 1 \) (since \( y \cdot -5 \neq 0 \) as long as \( y \neq 0 \))

Here are the final answers:

1. \( y^0 = 1 \)
2. \( - (y^0) = -1 \)
3. \( 0^0 = \text{undefined} \)
4. \( (-5)^0 = 1 \)
5. \( (y \cdot -5)^0 = 1 \)