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Simplify the expression: [tex]\(\frac{(a^8 \cdot a^6)^{\frac{1}{7}}}{a^2}\)[/tex].

[tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
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].
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