Question
What is the simplest form of 125 ^ (1/3) ? root(125 ^ 3, 1) 5 41.66 sqrt(125)
Answers
GPT-4o mini
The expression \( 125^{(1/3)} \) represents the cube root of 125.
To simplify this:
1. Recognize that \( 125 = 5^3 \).
2. Hence, \( 125^{(1/3)} = (5^3)^{(1/3)} \).
3. Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we have:
\[
(5^3)^{(1/3)} = 5^{3 \cdot (1/3)} = 5^1 = 5.
\]
So, the simplest form of \( 125^{(1/3)} \) is \( 5 \).
The other expressions you provided (like \( \sqrt{125} \), \( 41.66 \), and \( \text{root}(125^3, 1) \)) are not equivalent to \( 125^{(1/3)} \). The correct answer is:
\[
\boxed{5}.
\]
To simplify this:
1. Recognize that \( 125 = 5^3 \).
2. Hence, \( 125^{(1/3)} = (5^3)^{(1/3)} \).
3. Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we have:
\[
(5^3)^{(1/3)} = 5^{3 \cdot (1/3)} = 5^1 = 5.
\]
So, the simplest form of \( 125^{(1/3)} \) is \( 5 \).
The other expressions you provided (like \( \sqrt{125} \), \( 41.66 \), and \( \text{root}(125^3, 1) \)) are not equivalent to \( 125^{(1/3)} \). The correct answer is:
\[
\boxed{5}.
\]