To simplify the expression \( \frac{500a^4b^6}{10a^2b^3} \), let's break it down step by step.
-
Simplify the coefficients: \[ \frac{500}{10} = 50 \]
-
Simplify the \( a \) terms: \[ \frac{a^4}{a^2} = a^{4-2} = a^2 \]
-
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:
- \( 500a^4b^6 \)
- \( 10a^2b^3 \frac{3}{5} \)
- \( 5ab^2 \cdot 4a \)
- \( 10ab^2 \frac{3}{5a} \)
- \( 5a^2b^3 \frac{3}{4} \)
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: \[ \boxed{50a^2b^3} \]
1 answer