To simplify \( 512125\sqrt{3} \) using exponent properties, let's look at the expression step by step.
First, recognize that the square root can be represented using an exponent:
\[ \sqrt{3} = 3^{1/2} \]
Now we can rewrite the entire expression:
\[ 512125\sqrt{3} = 512125 \cdot 3^{1/2} \]
Next, we should analyze if \( 512125 \) can be expressed as a power of a base, but it actually does not appear to be a simple exponent of a whole number. Thus, we can leave \( 512125 \) as is for the moment.
However, if you want this in an alternate expression, you can keep it in the format:
\[ 512125 \cdot 3^{1/2} \]
We could also express this as:
\[ \frac{512125}{1} \cdot 3^{1/2} \]
Without additional options or a specific question to find a more simplified expression, it’s important to note that some expressions may combine numerical values or factor further. For a definitive equivalent expression, please provide specific options you are comparing, and I can assist you in identifying the equivalent one among your choices.
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