To simplify the expression \( 512125\sqrt{3} \) using exponent properties, let's break it down:
First, observe the number \( 512125 \) closely. It can be factored:
- \( 512 = 2^9 \)
- \( 125 = 5^3 \)
Thus, we can express \( 512125 \) as:
\[ 512125 = 2^9 \times 5^3 \]
Now, taking the square root of 3 gives:
\[ \sqrt{3} = 3^{1/2} \]
Combining these, we can rewrite the entire expression as:
\[ 512125\sqrt{3} = (2^9 \times 5^3) \times 3^{1/2} \]
Now let’s check what each response option simplifies to:
- 15 - This is a constant and does not relate to our expression.
- Start Fraction 1 over 5 End Fraction - This represents \( \frac{1}{5} \).
- 50 - This is a constant and does not relate to our expression.
- 5 superscript 0 baseline - \( 5^0 = 1 \).
- 5√5 - This does not directly relate to \( 512125\sqrt{3} \).
Now, let's reconsider the context—if \( 512125\sqrt{3} \) simplifies or reduces down to one of these options based solely on direct numerical value simplification or ratio without certain intermediary forms.
Given that none of these seem directly correlated to the expansions above or direct values, please confirm the expected context of further context or recheck for the exact question about simplification or equivalent properties.
Based on the current setup directly visible though, if looking for a direct numerical value, none fit and expressing in simpler forms without radical adjustments appears unclear. Thus the simplifications appear not to land onto the options given correctly.
Thus upon resolution :
The correct approach is noting there are no direct equivalences in the numerator rather just in forms or connective representations purely from \( 512125 \) to options given and needing a recalibration of values or reevaluation of the equivalent we're after.
If we're seeking that \( 512125 \) reduced matches \( \frac{1}{5} \) or \( 5^0\) directly without capture on intermediary step reductions, such should be reevaluated.
From cumulative analysis direct match does not yield clarity of direct reduction but rather number representations.
If forced to correlate directly there apparently seems no valid direct fit as was yet confirmed by numerical mappings visibly.