To simplify \( 512125\sqrt{3} \) using exponent properties, let's break it down:
First, recognize that \( 512125 \) can be factorized. If you factor it, you will find that:
\[ 512125 = 5^4 \cdot 3^1 \]
(You can verify this by performing the prime factorization of \( 512125 \)).
Now, the term \( \sqrt{3} \) can also be expressed using exponents:
\[ \sqrt{3} = 3^{1/2} \]
Now, rewriting \( 512125\sqrt{3} \):
\[ 512125\sqrt{3} = 5^4 \cdot 3^1 \cdot 3^{1/2} = 5^4 \cdot 3^{1 + 1/2} = 5^4 \cdot 3^{3/2} \]
The expression \( 512125\sqrt{3} \) does not appear to simplify to \( 50 \) or \( 1 \) or \( 15 \) or \( 5\sqrt{5} \).
You might want to check against the options given. However, without further context on how you would simplify \( 512125\sqrt{3} \) to a form that matches one of the answers, it seems that none of the options provided appears to be an equivalent expression of the original expression in the usual sense.
If you're looking for a specific choice among your options based on the context or intent (for example, if a specific assumption applies), please provide further clarification. Each option seems to represent a different mathematical structure from the original.
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