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Answer :
Let's work through the simplification step by step:
We need to simplify the expression [tex]\((5xy^5)^2(y^3)^4\)[/tex].
1. Simplify [tex]\((5xy^5)^2\)[/tex]:
- Apply the power to each component in the expression:
- [tex]\(5^2 = 25\)[/tex]
- [tex]\(x^2\)[/tex] (since [tex]\(x\)[/tex] is raised to the 1st power, and raised to another power of 2)
- [tex]\((y^5)^2 = y^{10}\)[/tex] (multiply the exponents: 5 times 2)
So, [tex]\((5xy^5)^2\)[/tex] simplifies to [tex]\(25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- [tex]\((y^3)^4 = y^{12}\)[/tex] (multiply the exponents: 3 times 4)
3. Combine the results:
Multiply the two simplified parts:
- [tex]\(25x^2y^{10} \times y^{12} = 25x^2y^{(10+12)} = 25x^2y^{22}\)[/tex]
The correct simplification of the expression is [tex]\(25x^2y^{22}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{25x^2y^{22}} \][/tex]
We need to simplify the expression [tex]\((5xy^5)^2(y^3)^4\)[/tex].
1. Simplify [tex]\((5xy^5)^2\)[/tex]:
- Apply the power to each component in the expression:
- [tex]\(5^2 = 25\)[/tex]
- [tex]\(x^2\)[/tex] (since [tex]\(x\)[/tex] is raised to the 1st power, and raised to another power of 2)
- [tex]\((y^5)^2 = y^{10}\)[/tex] (multiply the exponents: 5 times 2)
So, [tex]\((5xy^5)^2\)[/tex] simplifies to [tex]\(25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- [tex]\((y^3)^4 = y^{12}\)[/tex] (multiply the exponents: 3 times 4)
3. Combine the results:
Multiply the two simplified parts:
- [tex]\(25x^2y^{10} \times y^{12} = 25x^2y^{(10+12)} = 25x^2y^{22}\)[/tex]
The correct simplification of the expression is [tex]\(25x^2y^{22}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{25x^2y^{22}} \][/tex]
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