We are asked to evaluate the expression $0.3^{1/3} \times 0.3^{1/3} \times 0.3^{1/3}$.

AlgebraExponentsAlgebraic ManipulationReal Numbers
2025/5/19

1. Problem Description

We are asked to evaluate the expression 0.31/3×0.31/3×0.31/30.3^{1/3} \times 0.3^{1/3} \times 0.3^{1/3}.

2. Solution Steps

We have a product of three terms, each of which is 0.30.3 raised to the power of 1/31/3.
Using the property of exponents, which states that am×an=am+na^m \times a^n = a^{m+n}, we can combine the three terms.
0.31/3×0.31/3×0.31/3=0.3(1/3+1/3+1/3)0.3^{1/3} \times 0.3^{1/3} \times 0.3^{1/3} = 0.3^{(1/3 + 1/3 + 1/3)}
Now, we add the exponents:
1/3+1/3+1/3=3/3=11/3 + 1/3 + 1/3 = 3/3 = 1
Therefore, we have:
0.3(1/3+1/3+1/3)=0.31=0.30.3^{(1/3 + 1/3 + 1/3)} = 0.3^1 = 0.3

3. Final Answer

0. 3

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