Answer :
Certainly! Let's simplify the expression step-by-step.
We start with:
[tex]\[ 3 x^2 y^3 \cdot 4 x^3 y \][/tex]
1. Multiply the coefficients:
The coefficients are 3 and 4. Multiplying these,
[tex]\[ 3 \cdot 4 = 12 \][/tex]
2. Combine the [tex]\( x \)[/tex]-terms:
We have [tex]\( x^2 \)[/tex] and [tex]\( x^3 \)[/tex]. When multiplying terms with the same base, we add the exponents:
[tex]\[ x^2 \cdot x^3 = x^{2+3} = x^5 \][/tex]
3. Combine the [tex]\( y \)[/tex]-terms:
We have [tex]\( y^3 \)[/tex] and [tex]\( y \)[/tex]. Again, we add the exponents:
[tex]\[ y^3 \cdot y^1 = y^{3+1} = y^4 \][/tex]
Putting it all together, we get:
[tex]\[ 12 x^5 y^4 \][/tex]
So the simplified form of the expression is:
[tex]\[ \boxed{12 x^5 y^4} \][/tex]
This matches with option E.
We start with:
[tex]\[ 3 x^2 y^3 \cdot 4 x^3 y \][/tex]
1. Multiply the coefficients:
The coefficients are 3 and 4. Multiplying these,
[tex]\[ 3 \cdot 4 = 12 \][/tex]
2. Combine the [tex]\( x \)[/tex]-terms:
We have [tex]\( x^2 \)[/tex] and [tex]\( x^3 \)[/tex]. When multiplying terms with the same base, we add the exponents:
[tex]\[ x^2 \cdot x^3 = x^{2+3} = x^5 \][/tex]
3. Combine the [tex]\( y \)[/tex]-terms:
We have [tex]\( y^3 \)[/tex] and [tex]\( y \)[/tex]. Again, we add the exponents:
[tex]\[ y^3 \cdot y^1 = y^{3+1} = y^4 \][/tex]
Putting it all together, we get:
[tex]\[ 12 x^5 y^4 \][/tex]
So the simplified form of the expression is:
[tex]\[ \boxed{12 x^5 y^4} \][/tex]
This matches with option E.
