Answer :
Let's simplify the expression [tex]\(3x^2 y^3 \cdot 4x^3 y\)[/tex] step by step.
1. Multiply the coefficients:
The coefficients in the expression are 3 and 4.
Multiply them: [tex]\(3 \times 4 = 12\)[/tex].
2. Add the exponents for [tex]\(x\)[/tex]:
[tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex] are the powers of [tex]\(x\)[/tex] in the expression.
To combine them, add the exponents: [tex]\(2 + 3 = 5\)[/tex].
So, the exponent for [tex]\(x\)[/tex] in the simplified expression is [tex]\(x^5\)[/tex].
3. Add the exponents for [tex]\(y\)[/tex]:
[tex]\(y^3\)[/tex] and [tex]\(y^1\)[/tex] (remember, [tex]\(y\)[/tex] is the same as [tex]\(y^1\)[/tex]) are the powers of [tex]\(y\)[/tex].
Add the exponents: [tex]\(3 + 1 = 4\)[/tex].
So, the exponent for [tex]\(y\)[/tex] in the simplified expression is [tex]\(y^4\)[/tex].
Putting it all together, the simplified form of the expression is:
[tex]\[12x^5 y^4\][/tex]
Therefore, the correct answer is option E. [tex]\(12x^5 y^4\)[/tex].
1. Multiply the coefficients:
The coefficients in the expression are 3 and 4.
Multiply them: [tex]\(3 \times 4 = 12\)[/tex].
2. Add the exponents for [tex]\(x\)[/tex]:
[tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex] are the powers of [tex]\(x\)[/tex] in the expression.
To combine them, add the exponents: [tex]\(2 + 3 = 5\)[/tex].
So, the exponent for [tex]\(x\)[/tex] in the simplified expression is [tex]\(x^5\)[/tex].
3. Add the exponents for [tex]\(y\)[/tex]:
[tex]\(y^3\)[/tex] and [tex]\(y^1\)[/tex] (remember, [tex]\(y\)[/tex] is the same as [tex]\(y^1\)[/tex]) are the powers of [tex]\(y\)[/tex].
Add the exponents: [tex]\(3 + 1 = 4\)[/tex].
So, the exponent for [tex]\(y\)[/tex] in the simplified expression is [tex]\(y^4\)[/tex].
Putting it all together, the simplified form of the expression is:
[tex]\[12x^5 y^4\][/tex]
Therefore, the correct answer is option E. [tex]\(12x^5 y^4\)[/tex].
