Question
Fully simplify (z6)0⋅z5\left(z^{6}\right)^{0}\cdot z^{5}(z
6
)
0
⋅z
5
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Answers
GPT-4o mini
To simplify the expression \((z^{6})^{0} \cdot z^{5}\), we can follow the rules of exponents.
1. **Exponent Rule**: Any non-zero number raised to the power of zero is equal to 1. Therefore, we have:
\[
(z^{6})^{0} = 1
\]
2. Now, substituting this back into the expression gives:
\[
1 \cdot z^{5}
\]
3. Next, simplifying this results in:
\[
z^{5}
\]
Thus, the fully simplified expression is:
\[
\boxed{z^{5}}
\]
1. **Exponent Rule**: Any non-zero number raised to the power of zero is equal to 1. Therefore, we have:
\[
(z^{6})^{0} = 1
\]
2. Now, substituting this back into the expression gives:
\[
1 \cdot z^{5}
\]
3. Next, simplifying this results in:
\[
z^{5}
\]
Thus, the fully simplified expression is:
\[
\boxed{z^{5}}
\]