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
5 superscript 0 baseline

Answer 1

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:

1. **5√5**
- Not an equivalent expression to \( 5^7 \cdot 3^{1/2} \).

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.

3. **15**
- Not an equivalent expression.

4. **Start Fraction 1 over 5 End Fraction**
- This is \( 5^{-1} \), which is not equivalent.

5. **1**
- This is not an equivalent expression.

6. **50**
- Writing it as \( 5^1 \cdot 10^1 \), which still doesn’t match.

7. **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.