To determine which expression is equivalent to [tex]\(\left(a^8\right)^4\)[/tex], we'll use the properties of exponents.
When you have an expression of the form [tex]\(\left(a^m\right)^n\)[/tex], you can simplify it using the power rule of exponents, which states that [tex]\(\left(a^m\right)^n = a^{m \cdot n}\)[/tex].
In this case, we have [tex]\(\left(a^8\right)^4\)[/tex].
Using the power rule of exponents, we multiply the exponents [tex]\(8\)[/tex] and [tex]\(4\)[/tex]:
[tex]\[ \left(a^8\right)^4 = a^{8 \cdot 4} \][/tex]
Next, we calculate the product of [tex]\(8\)[/tex] and [tex]\(4\)[/tex]:
[tex]\[ 8 \cdot 4 = 32 \][/tex]
So, [tex]\(\left(a^8\right)^4\)[/tex] simplifies to [tex]\(a^{32}\)[/tex].
Therefore, the expression equivalent to [tex]\(\left(a^8\right)^4\)[/tex] is [tex]\(a^{32}\)[/tex].
The correct answer is:
[tex]\[ a^{32} \][/tex]
