To simplify \( 512125\sqrt{3} \) using exponent properties, we first look at the term \( 512125 \).
The number \( 512125 \) can be factored as follows:
- It is the result of \( 5^5 \) since \( 5^5 = 3125 \) and \( 5^6 = 15625 \).
- More specifically, \( 512125 = 5^5 \times 3^1 \) since \( 512125 = 5^5 \cdot \sqrt{3} \).
Now, we can rewrite the expression:
\[ 512125\sqrt{3} = 5^5 \times \sqrt{3} \]
Using the property of square roots, we can express \( \sqrt{3} \) as \( 3^{1/2} \):
\[ = 5^5 \times 3^{1/2} \]
This does not simplify directly into one of the multiple choice answers you've provided. However, since you are asking for equivalence in simpler terms, let's check each option based on their equivalent value:
- 15: Not equal to \( 512125\sqrt{3} \)
- Start Fraction \( 1 \) over \( 5 \) End Fraction: Not equal to \( 512125\sqrt{3} \)
- \( 5\sqrt{5} \): Not equal to \( 512125\sqrt{3} \)
- Start Fraction Start Root \( 5 \) End Root over \( 5 \) End Fraction: Not equal to \( 512125\sqrt{3} \)
- 1: Not equal to \( 512125\sqrt{3} \)
- 50: Not equal to \( 512125\sqrt{3} \)
- \( 5^0 \): Equal to 1.
Since none of these options appear to be equivalent to \( 512125\sqrt{3} \), it may be a misunderstanding of the question. If we consider mathematical expressions that might equal similar power forms or calculations, \( 50 \) or actions linked to it could work.
However, based on simplification and clarity, it seems neither of the choices you presented directly corresponds to \( 512125\sqrt{3} \), and none of the choices listed matches it in any clear exponent properties or sums.
Please double-check the question for any additional detail or confirm the expression itself if this seems misaligned.