To simplify the expression [tex]\(\left(a^8\right)^{\frac{1}{2}}\)[/tex], we can use the power of a power property of exponents. This property states that [tex]\(\left(a^m\right)^n = a^{m \cdot n}\)[/tex].
Here are the steps to simplify the expression:
1. Identify the outer exponent and the inner exponent. In this case, the outer exponent is [tex]\(\frac{1}{2}\)[/tex] and the inner exponent is [tex]\(8\)[/tex].
2. Multiply the exponents together: [tex]\(8 \cdot \frac{1}{2}\)[/tex].
3. Perform the multiplication: [tex]\(8 \cdot \frac{1}{2} = 4\)[/tex].
So, the simplified form of the expression [tex]\(\left(a^8\right)^{\frac{1}{2}}\)[/tex] is [tex]\(a^4\)[/tex].
Answer: [tex]\(a^4\)[/tex]
