Which of the following is an equivalent expression for 512125√3 when simplified using exponent properties?(1 point)

Question

Responses

1
1

15
Start Fraction 1 over 5 End Fraction

50
5 superscript 0 baseline

5√5
Start Fraction Start Root 5 End Root over 5 End Fraction

Answer 1

To simplify \( 512125\sqrt{3} \) using exponent properties, let's first factor \( 512125 \).

1. \( 512125 \) can be factored as \( 5^5 \) (since \( 5^5 = 3125 \) and the rest of the prime factorization adds up to \( 512125 \)), giving \( 5^5 \times \sqrt{3} \).
2. We express \( \sqrt{3} \) as \( 3^{1/2} \).
3. Therefore, we can treat the whole expression as \( 5^5 \times 3^{1/2} \).

Now, let's examine the options provided:

1. 1 - This is not equivalent to our expression.
2. Start Fraction 1 over 5 End Fraction - This would be \( 5^{-1} \), which is not equal to our expression.
3. 50 - This is not equivalent to our expression.
4. Start Fraction Start Root 5 End Root over 5 End Fraction - This simplifies to \( \frac{\sqrt{5}}{5} \), which is also not equivalent to our expression.

Since none of the answers given directly correspond to \( 5^5 \) or \( 5^5 \sqrt{3} \), and since \( \sqrt{3} \) doesn't have a direct match, it appears none of the options correctly simplifies to an equivalent expression for \( 512125\sqrt{3} \).

Please check the options again or clarify if additional choices are available.