Question

Apply properties of operations to multiply 5a2b5c3⋅−4a7c5 .(1 point) Responses 20a9b5c8 20 a superscript 9 baseline b superscript 5 baseline c superscript 8 baseline −20a9b5c8 negative 20 a superscript 9 baseline b superscript 5 baseline c superscript 8 baseline 20a14b5c15 20 a superscript 14 baseline b superscript 5 baseline c superscript 15 baseline −20a14b5c15

Answer 1

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

1. Multiply the coefficients: \(5 \times -4 = -20\)

2. Multiply the variables:

   • For \(a\): \(a^2 \times a^7 = a^{2+7} = a^9\)
   • For \(b\): \(b^5 \) (since there is no \(b\) term in the second expression, it remains \(b^5\))
   • For \(c\): \(c^3 \times c^5 = c^{3+5} = c^8\)

Putting all these together, we obtain:

\[ -20a^9b^5c^8 \]

So the final expression after multiplying \(5a^2b^5c^3\) by \(-4a^7c^5\) is:

\(-20a^9b^5c^8\)

The correct response is: \(-20a^9b^5c^8\)