Apply properties of operations to multiply 5a2b5c3⋅−4a7c5

Question

.(1 point)
Responses

−20a14b5c15
negative 20 a superscript 14 baseline b superscript 5 baseline c superscript 15 baseline

20a14b5c15
20 a superscript 14 baseline b superscript 5 baseline c superscript 15 baseline

−20a9b5c8
negative 20 a superscript 9 baseline b superscript 5 baseline c superscript 8 baseline

20a9b5c8

Answer 1

To multiply the expressions \(5a^2b^5c^3\) and \(-4a^7c^5\), we can follow these steps:

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

2. Multiply the variables by adding their exponents:

   • For \(a\): \[ a^2 \cdot a^7 = a^{2+7} = a^9 \]
   • For \(b\): \[ b^5 \text{ (there is no } b \text{ in the second expression, so it remains as } b^5) \]
   • For \(c\): \[ c^3 \cdot c^5 = c^{3+5} = c^8 \]

Now, combine all the results: \[ -20a^9b^5c^8 \]

Thus, the final answer is: \[ \text{negative } 20a^9b^5c^8 \]

The response that corresponds to this result is: \[ \text{negative } 20 a^{9} b^{5} c^{8} \]