To simplify the expression [tex]\(\left(x^4\right)^8\)[/tex], we can apply the power rule of exponents, which states that [tex]\((x^a)^b = x^{a \cdot b}\)[/tex].
Here, the base [tex]\(x\)[/tex] is raised to the power of 4, and this entire expression is then raised to the power of 8. According to the power rule:
[tex]\[
(x^4)^8 = x^{4 \cdot 8}
\][/tex]
Next, we multiply the exponents:
[tex]\[
4 \cdot 8 = 32
\][/tex]
Thus, the simplest form of [tex]\(\left(x^4\right)^8\)[/tex] is:
[tex]\[
x^{32}
\][/tex]
Therefore, the expression [tex]\(\left(x^4\right)^8\)[/tex] in simplest form is [tex]\(x^{32}\)[/tex].
