Question

Simplify 500a4b6 (1 point)
10a²b³ 3/5
5ab² 4a
10ab² 3/5a
5a²b³ 3/4

Answer 1

To simplify the expression \( \frac{500a^4b^6}{10a^2b^3} \), let's break it down step by step.

1. **Simplify the coefficients:**
\[
\frac{500}{10} = 50
\]

2. **Simplify the \( a \) terms:**
\[
\frac{a^4}{a^2} = a^{4-2} = a^2
\]

3. **Simplify the \( b \) terms:**
\[
\frac{b^6}{b^3} = b^{6-3} = b^3
\]

Putting it all together:
\[
\frac{500a^4b^6}{10a^2b^3} = 50a^2b^3
\]

Now, let's compare this with the given options:

1. \( 500a^4b^6 \)
2. \( 10a^2b^3 \frac{3}{5} \)
3. \( 5ab^2 \cdot 4a \)
4. \( 10ab^2 \frac{3}{5a} \)
5. \( 5a^2b^3 \frac{3}{4} \)

None of the options directly match \( 50a^2b^3 \).

However, we can manipulate \( 50a^2b^3 \) to check if any options are potentially equivalent to it.

### Checking Option 2:
\[
10a^2b^3 \cdot \frac{3}{5} = \frac{3 \cdot 10a^2b^3}{5} = 6a^2b^3
\]
This does not match.

### Checking Option 3:
\[
5ab^2 \cdot 4a = 20a^2b^2
\]
This does not match.

### Checking Option 4:
\[
10ab^2 \cdot \frac{3}{5a} = 6b^2
\]
This does not match.

### Checking Option 5:
\[
5a^2b^3 \cdot \frac{3}{4} = \frac{15}{4}a^2b^3
\]
This does not match either.

### Conclusion:
None of the provided options are equivalent to \( 50a^2b^3 \), or there may have been a misunderstanding in how the options are presented or a different question intended.

For the expression \( \frac{500a^4b^6}{10a^2b^3} \), the simplified result remains:
\[
\boxed{50a^2b^3}
\]