Question

Apply properties of operations to multiply 5a^2b^5c^3 x -4a^7c^5

Answer 1

To multiply the expressions \( 5a^2b^5c^3 \) and \(-4a^7c^5\), we will follow the properties of operations, particularly the distributive property and the properties of exponents.

1. **Multiply the coefficients**:
- The coefficients are \(5\) and \(-4\).
- Multiplying these gives:
\[
5 \times -4 = -20.
\]

2. **Multiply the variables**:
- For variable \(a\):
\[
a^2 \times a^7 = a^{2+7} = a^9 \quad \text{(adding the exponents)}.
\]
- For variable \(b\):
- Since \(b\) only appears in the first term, it remains as is:
\[
b^5.
\]
- For variable \(c\):
\[
c^3 \times c^5 = c^{3+5} = c^8 \quad \text{(adding the exponents)}.
\]

3. **Combine the results**:
Combining all parts, we have:
\[
-20a^9b^5c^8.
\]

Thus, the result of multiplying \( 5a^2b^5c^3 \) and \(-4a^7c^5\) is:
\[
\boxed{-20a^9b^5c^8}.
\]