To simplify the expression [tex]\(\left(z^8\right)^2\)[/tex]:
1. Understand the Exponentiation Rule:
When raising a power to another power, you multiply the exponents. This is known as the power of a power property in exponents.
2. Apply the Rule:
Here, we have [tex]\(\left(z^8\right)^2\)[/tex]. According to the power of a power property, this becomes:
[tex]\[
z^{8 \times 2}
\][/tex]
3. Multiply the Exponents:
Multiply 8 by 2 to get:
[tex]\[
8 \times 2 = 16
\][/tex]
4. Write the Final Simplified Expression:
Therefore, the simplified form of [tex]\(\left(z^8\right)^2\)[/tex] is:
[tex]\[
z^{16}
\][/tex]
So, the answer is:
[tex]\[
\boxed{z^{16}}
\][/tex]
