To simplify the expression [tex]\(\frac{\left(a^8 a^6\right)^{\frac{1}{7}}}{a^2}\)[/tex], follow these steps:
1. Combine the exponents inside the parentheses:
[tex]\[
a^8 \cdot a^6 = a^{8+6} = a^{14}
\][/tex]
2. Apply the outer exponent to the result:
[tex]\[
\left(a^{14}\right)^{\frac{1}{7}} = a^{14 \cdot \frac{1}{7}} = a^2
\][/tex]
3. Divide by the denominator exponent:
[tex]\[
\frac{a^2}{a^2} = a^{2-2} = a^0
\][/tex]
4. Simplify the final result:
[tex]\[
a^0 = 1
\][/tex]
Thus, the simplified expression is [tex]\(1\)[/tex].
