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Answer :
To simplify the expression [tex]\(3x^2y^3 \cdot 4x^3y\)[/tex], we will follow these steps:
1. Multiply the coefficients:
- The coefficients in the expression are 3 and 4.
- Multiply them together: [tex]\(3 \cdot 4 = 12\)[/tex].
2. Apply the rules of exponents to [tex]\(x\)[/tex] terms:
- You have [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex].
- When multiplying like bases, add the exponents: [tex]\(x^{2+3} = x^5\)[/tex].
3. Apply the rules of exponents to [tex]\(y\)[/tex] terms:
- You have [tex]\(y^3\)[/tex] and [tex]\(y\)[/tex] (which is equivalent to [tex]\(y^1\)[/tex]).
- Add the exponents: [tex]\(y^{3+1} = y^4\)[/tex].
Now, combine everything:
- The simplified expression is [tex]\(12x^5y^4\)[/tex].
So, the correct answer is E. [tex]\(12x^5y^4\)[/tex].
1. Multiply the coefficients:
- The coefficients in the expression are 3 and 4.
- Multiply them together: [tex]\(3 \cdot 4 = 12\)[/tex].
2. Apply the rules of exponents to [tex]\(x\)[/tex] terms:
- You have [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex].
- When multiplying like bases, add the exponents: [tex]\(x^{2+3} = x^5\)[/tex].
3. Apply the rules of exponents to [tex]\(y\)[/tex] terms:
- You have [tex]\(y^3\)[/tex] and [tex]\(y\)[/tex] (which is equivalent to [tex]\(y^1\)[/tex]).
- Add the exponents: [tex]\(y^{3+1} = y^4\)[/tex].
Now, combine everything:
- The simplified expression is [tex]\(12x^5y^4\)[/tex].
So, the correct answer is E. [tex]\(12x^5y^4\)[/tex].
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