Apply properties of operations to multiply 5a^2b^5c^3⋅−4a^7c^5 .

1 answer

To multiply the expression \(5a^2b^5c^3 \cdot -4a^7c^5\), we follow the properties of operations, particularly the properties of multiplication and the laws of exponents.

  1. Multiply the coefficients (numerical parts): \[ 5 \cdot -4 = -20 \]

  2. Multiply the variables with the same base by adding their exponents:

    • For \(a\): \[ a^2 \cdot a^7 = a^{2+7} = a^9 \]
    • For \(b\): \[ b^5 \cdot b^0 = b^5 \quad (\text{since } b^0 = 1) \]
    • For \(c\): \[ c^3 \cdot c^5 = c^{3+5} = c^8 \]
  3. Combine all parts together: Now, we can write the final result: \[ -20a^9b^5c^8 \]

So, the simplified result of the multiplication \(5a^2b^5c^3 \cdot -4a^7c^5\) is: \[ \boxed{-20a^9b^5c^8} \]