We are asked to evaluate the expression $\sqrt[7]{(10)^7}$ if possible, and if the result is a real number.

AlgebraExponentsRootsSimplification
2025/4/21

1. Problem Description

We are asked to evaluate the expression (10)77\sqrt[7]{(10)^7} if possible, and if the result is a real number.

2. Solution Steps

The expression (10)77\sqrt[7]{(10)^7} can be written as (107)1/7(10^7)^{1/7}.
Using the property of exponents, we have:
(am)n=amn(a^m)^n = a^{m*n}
Therefore, (107)1/7=107(1/7)=101=10(10^7)^{1/7} = 10^{7*(1/7)} = 10^1 = 10.
Since 10 is a real number, the answer is
1
0.

3. Final Answer

The answer is 10.

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