Answer :
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].
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].
