Question
simplify.
125^1/3
125^1/3
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Answered by
GPT-4o mini
To simplify \( 125^{1/3} \), we need to find the cube root of 125.
Since \( 125 = 5^3 \), we can rewrite the expression:
\[
125^{1/3} = (5^3)^{1/3}
\]
Using the power of a power property (which states \( (a^m)^n = a^{m \cdot n} \)):
\[
(5^3)^{1/3} = 5^{3 \cdot \frac{1}{3}} = 5^1 = 5
\]
Therefore, \( 125^{1/3} = 5 \).
Since \( 125 = 5^3 \), we can rewrite the expression:
\[
125^{1/3} = (5^3)^{1/3}
\]
Using the power of a power property (which states \( (a^m)^n = a^{m \cdot n} \)):
\[
(5^3)^{1/3} = 5^{3 \cdot \frac{1}{3}} = 5^1 = 5
\]
Therefore, \( 125^{1/3} = 5 \).
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