What is 4a^6 b^5 c^4 * −7b^7 c^6

Question

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Answer 1

To multiply the expressions $4a^6{b}^5{c}^4$ and $-7b^7{c}^6$, you can follow these steps:

1. Multiply the coefficients: $4$ and $-7$: $$4\cdot -7=-28$$

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

   • For $b$: $$b^5\cdot b^7=b^{5+7}=b^{12}$$

   • For $c$: $$c^4\cdot c^6=c^{4+6}=c^{10}$$

3. The variable $a$ only comes from the first term, so it remains $a^6$.

Now, combine all parts together: $$4a^6{b}^5{c}^4\cdot -7b^7{c}^6=-28a^6{b}^{12}{c}^{10}$$

Thus, the result is: $$\boxed{{\displaystyle -28a^6{b}^{12}{c}^{10}}}$$