Sure, let's simplify the given expression step by step:
Given expression:
[tex]\[
5a b c \times 2a b^2 c^3 \times 3a c
\][/tex]
### Step 1: Group the coefficients
First, let's group all the numerical coefficients:
[tex]\[
5 \times 2 \times 3
\][/tex]
Multiplying these together:
[tex]\[
5 \times 2 = 10
\][/tex]
[tex]\[
10 \times 3 = 30
\][/tex]
So, the combined coefficient is [tex]\(30\)[/tex].
### Step 2: Group like terms for each variable
Now, let's group the like terms for each variable:
For [tex]\(a\)[/tex]:
[tex]\[
a \times a \times a = a^3
\][/tex]
For [tex]\(b\)[/tex]:
[tex]\[
b \times b^2 = b^3
\][/tex]
For [tex]\(c\)[/tex]:
[tex]\[
c \times c^3 \times c = c^5
\][/tex]
### Step 3: Combine the results
Combining the coefficient and the variables, we get:
[tex]\[
30a^3 b^3 c^5
\][/tex]
So, the simplified expression is:
[tex]\[
30a^3 b^3 c^5
\][/tex]
This detailed step-by-step process leads to the result [tex]\(30a^3 b^3 c^5\)[/tex].
