To simplify the expression \( 512125\sqrt{3} \) using exponent properties, we start by recognizing that the square root can be expressed as an exponent:
\[ \sqrt{3} = 3^{1/2} \]
Thus, we can rewrite the expression as:
\[ 512125 \cdot 3^{1/2} \]
Next, we can express \( 512125 \) as a power of another base if possible. Upon factoring, we find that:
\[ 512125 = 5^4 \cdot 11^2 \]
So now the expression becomes:
\[ 5^4 \cdot 11^2 \cdot 3^{1/2} \]
As a result, we do not have an equivalent form with a single base unless specified otherwise.
If you're looking for a simplified form or a combined exponent:
\[ 512125\sqrt{3} = 5^4 \cdot 11^2 \cdot 3^{1/2} \]
This maintains the numeric integrity of the expression while leveraging exponent properties.
If you have multiple-choice responses or require further transformation options, please provide them!
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