To simplify the expression \( 512125\sqrt{3} \), we first convert \( 512125 \) into its prime factorization:
- \( 512125 \) can be factored as \( 5^4 \times 3^2 \).
Next, we simplify \( 512125 \sqrt{3} \):
\[ 512125\sqrt{3} = 5^4 \times 3^2 \times \sqrt{3} = 5^4 \times 3^{2 + \frac{1}{2}} = 5^4 \times 3^{\frac{5}{2}} \]
To express this in terms of exponent properties, we can write \( 3^{\frac{5}{2}} \) as:
\[ 3^2 \times \sqrt{3} = 9\sqrt{3} \]
Thus, we have:
\[ 512125\sqrt{3} = 5^4 \times 9\sqrt{3} = 625 \times 9\sqrt{3} = 5625\sqrt{3} \]
Now let's analyze the answers provided:
- 15: Doesn't match.
- Start Fraction 1 over 5 End Fraction: Doesn't match.
- 5√5: Doesn't match.
- Start Fraction Start Root 5 End Root over 5 End Fraction: Doesn't match.
- 50: Doesn't match.
- 5 superscript 0 baseline: This is equal to 1, which doesn't match.
- 1: This doesn't match.
None of the provided answers appear to match the simplified version of \( 512125\sqrt{3} \).
If we take a different approach using the properties of exponents, we can see that \( 512125 \) can also be more simply understood.
To answer your question, none of the responses you provided are equivalent to \( 512125\sqrt{3} \). Please double-check the options, or provide more context if there are more specific choices.
1 answer