To simplify \( 512125\sqrt{3} \) using exponent properties, let's first rewrite \( 512125 \) in exponential form if possible.
\( 512125 = 5^7 \cdot 3^0 \).
Now, we can express \( \sqrt{3} \) as \( 3^{1/2} \).
Now combine these:
\[ 512125\sqrt{3} = 5^7 \cdot 3^{1/2} \]
At this point, our expression is \( 5^7 \cdot 3^{1/2} \). Now we can see this doesn’t directly match the given choices.
Let’s analyze each of the choices provided:
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5√5
- Not an equivalent expression to \( 5^7 \cdot 3^{1/2} \).
-
Start Fraction Start Root 5 End Root over 5 End Fraction
- This is equivalent to \( \frac{\sqrt{5}}{5} = 5^{-1/2} \), which is not equivalent.
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15
- Not an equivalent expression.
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Start Fraction 1 over 5 End Fraction
- This is \( 5^{-1} \), which is not equivalent.
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1
- This is not an equivalent expression.
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50
- Writing it as \( 5^1 \cdot 10^1 \), which still doesn’t match.
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5 superscript 0 baseline
- This is equivalent to \( 1 \).
The given options do not seem to have a perfect equivalent from \( 512125\sqrt{3} \), since \( 5^7 \cdot 3^{1/2} \) is quite larger.
Since the expression is \( 5^7 \cdot 3^{1/2} \) and no options directly correlate with the components of the exponent, it may require a reconsideration of the options provided or assessing if additional simplifications have been missed.
From analyzing the available choices closely, most appear not to correlate directly with \( 512125\sqrt{3} \). If the primary goal was simplification, and either confirming specific values or close ranges by evaluating specific powers may yield a useful answer given the structure.