To simplify the expression [tex]\(\frac{\left(a^8 a^6\right)^{\frac{1}{7}}}{a^2}\)[/tex], let's go through the steps:
1. Combine the exponents inside the numerator:
[tex]\[
a^8 \cdot a^6 = a^{8+6} = a^{14}
\][/tex]
2. Apply the outer exponent to the base:
[tex]\[
\left(a^{14}\right)^{\frac{1}{7}} = a^{14 \cdot \frac{1}{7}} = a^2
\][/tex]
3. Substitute this back into the expression:
[tex]\[
\frac{a^2}{a^2}
\][/tex]
4. Simplify the fraction:
[tex]\[
a^2 \div a^2 = 1
\][/tex]
Therefore, the simplified expression is:
[tex]\[
1
\][/tex]
