Answer :
To simplify the expression [tex]\(3x^2y^3 \cdot 4x^3y\)[/tex], follow these steps:
1. Multiply the constants:
- Multiply the numerical coefficients: [tex]\(3 \times 4 = 12\)[/tex].
2. Multiply the [tex]\(x\)[/tex]-terms:
- You have [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex]. When you multiply terms with the same base, you add the exponents:
[tex]\[
x^2 \cdot x^3 = x^{2+3} = x^5
\][/tex]
3. Multiply the [tex]\(y\)[/tex]-terms:
- You have [tex]\(y^3\)[/tex] and [tex]\(y^1\)[/tex] (since [tex]\(y\)[/tex] is the same as [tex]\(y^1\)[/tex]). Add the exponents:
[tex]\[
y^3 \cdot y^1 = y^{3+1} = y^4
\][/tex]
After multiplying the components together, the simplified expression is:
[tex]\[
12x^5y^4
\][/tex]
From the provided options, this corresponds to option E.
1. Multiply the constants:
- Multiply the numerical coefficients: [tex]\(3 \times 4 = 12\)[/tex].
2. Multiply the [tex]\(x\)[/tex]-terms:
- You have [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex]. When you multiply terms with the same base, you add the exponents:
[tex]\[
x^2 \cdot x^3 = x^{2+3} = x^5
\][/tex]
3. Multiply the [tex]\(y\)[/tex]-terms:
- You have [tex]\(y^3\)[/tex] and [tex]\(y^1\)[/tex] (since [tex]\(y\)[/tex] is the same as [tex]\(y^1\)[/tex]). Add the exponents:
[tex]\[
y^3 \cdot y^1 = y^{3+1} = y^4
\][/tex]
After multiplying the components together, the simplified expression is:
[tex]\[
12x^5y^4
\][/tex]
From the provided options, this corresponds to option E.
