Question

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

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

15
Start Fraction 1 over 5 End Fraction

1
1

50

Answer 1

To simplify the expression \( 512125\sqrt{3} \) using exponent properties, let's first rewrite \( 512125 \) in terms of its prime factors:

Calculating the prime factorization:
- \( 512 = 2^9 \)
- \( 125 = 5^3 \)

Thus, \( 512125 = 2^9 \times 5^3 \). Now we can multiply by \( \sqrt{3} \):

\[
512125\sqrt{3} = (2^9 \times 5^3) \times 3^{1/2}
\]

Now, we look for an equivalent expression from the options given. However, the options do not seem directly relatable without further context about preferred forms.

The options given are:
1. \( 5\sqrt{5} \)
2. \( \frac{\sqrt{5}}{5} \)
3. \( 15 \)
4. \( \frac{1}{5} \)
5. \( 1 \)
6. \( 50 \)

Since none of those options appear obviously related to \( 512125\sqrt{3} \), we may need to evaluate if one of these can be derived or simplified from the expression. However, this simplification needs more processing, including possible translations to simpler forms or values:

The further evaluation does not directly approach \( 512125\sqrt{3} \) and I don't see immediate equivalence without numerical approximation or transformation.

If treated purely in numeric evaluations, one needs to verify by approximating the value of \( 512125 \) with respect to options just to confirm numerical proximity.

Since \( 512125\sqrt{3} \approx 512125 \times 1.732 \) what would need checking against the numeric values inferred from options; however, this seems excessive without further constraints.

In conclusion, none of the options represent an immediate equivalence without further explicit context or prompts that directly relate outputs to transformations or manipulations equating \( 512125\sqrt{3} \).

If forced to choose without a clear pathway among numeric approximations, I would recommend consulting further because a direct simple form exists with expansion or rounded numerical processes to define exact simplifications around value transformations. Further, those imply external rational processes not straightforward visibly in provided responses.

Would need specified context whether accommodating divisions or growth against power basis carefully delineated!