Certainly! Let's break down the expression step by step to solve it.
Given expression: [tex]\((7a^2)(3a^3(-2a))\)[/tex]
1. Simplify inside the parentheses first:
[tex]\[
3a^3(-2a)
\][/tex]
- Multiply the coefficients: [tex]\( 3 \times -2 = -6 \)[/tex]
- For the terms involving [tex]\(a\)[/tex], apply the laws of exponents: [tex]\( a^3 \times a = a^{3+1} = a^4 \)[/tex]
Therefore,
[tex]\[
3a^3(-2a) = -6a^4
\][/tex]
2. Now multiply the simplified result by [tex]\(7a^2\)[/tex]:
[tex]\[
(7a^2)(-6a^4)
\][/tex]
- Multiply the coefficients: [tex]\( 7 \times -6 = -42 \)[/tex]
- For the terms involving [tex]\(a\)[/tex], apply the laws of exponents: [tex]\( a^2 \times a^4 = a^{2+4} = a^6 \)[/tex]
Therefore,
[tex]\[
(7a^2)(-6a^4) = -42a^6
\][/tex]
So the final expression simplifies to [tex]\(-42a^6\)[/tex].
The numerical portion of the result is [tex]\(-42\)[/tex].
