Let's solve each part of the question step-by-step, using the rule that any non-zero number raised to the zero power is [tex]\(1\)[/tex].
a) [tex]\((-6)^0\)[/tex]
According to the zero exponent rule, any non-zero number raised to the zero power is [tex]\(1\)[/tex]:
[tex]\[ (-6)^0 = 1 \][/tex]
b) [tex]\(x^0\)[/tex] and [tex]\(a^0\)[/tex]
Similarly:
[tex]\[ x^0 = 1 \][/tex]
[tex]\[ a^0 = 1 \][/tex]
c) [tex]\(-(7)^0\)[/tex]
Here, [tex]\(7^0\)[/tex] is calculated first, which is [tex]\(1\)[/tex]. Then, the negative sign is applied:
[tex]\[ -(7)^0 = -(1) = -1 \][/tex]
For the additional parts within section c:
[tex]\[ 3^0 = 1 \][/tex]
[tex]\[ (-3)^0 = 1 \ (since -3 is treated as a base and any non-zero number to the power of 0 is still 1) \][/tex]
[tex]\[ x^0 = 1 \][/tex]
d) [tex]\((25xyz)^0\)[/tex]
Regardless of the values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex], as long as none of them are zero, the entire expression to the power of zero is [tex]\(1\)[/tex]:
[tex]\[ (25xyz)^0 = 1 \][/tex]
e) [tex]\(y^0\)[/tex]
[tex]\[ y^0 = 1 \][/tex]
f) [tex]\(\text{word}^0\)[/tex]
Assuming "word" is a non-zero variable:
[tex]\[ \text{word}^0 = 1 \][/tex]
In conclusion, applying the zero exponent rule accurately:
[tex]\[ (-6)^0 = 1 \][/tex]
[tex]\[ x^0 = 1 \][/tex]
[tex]\[ a^0 = 1 \][/tex]
[tex]\[ -(7)^0 = -1 \][/tex]
[tex]\[ 3^0 = 1 \][/tex]
[tex]\[ (-3)^0 = 1 \][/tex]
[tex]\[ x^0 = 1 \][/tex]
[tex]\[ (25xyz)^0 = 1 \][/tex]
[tex]\[ y^0 = 1 \][/tex]
[tex]\[ \text{word}^0 = 1 \][/tex]
