Answer :
To simplify the expression [tex]\((5xy^5)^2(y^3)^4\)[/tex], let's break it down step by step:
1. Simplify the first part [tex]\((5xy^5)^2\)[/tex]:
- The expression [tex]\((5xy^5)^2\)[/tex] is being squared.
- First, square the coefficient: [tex]\(5^2 = 25\)[/tex].
- Next, apply the power of 2 to [tex]\(x\)[/tex]: [tex]\((x)^2 = x^2\)[/tex].
- Finally, apply the power of 2 to [tex]\(y^5\)[/tex]: [tex]\((y^5)^2 = y^{5 \times 2} = y^{10}\)[/tex].
So the result of [tex]\((5xy^5)^2\)[/tex] is [tex]\(25x^2y^{10}\)[/tex].
2. Simplify the second part [tex]\((y^3)^4\)[/tex]:
- Here, apply the power of 4 to [tex]\(y^3\)[/tex]: [tex]\((y^3)^4 = y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the simplified parts:
- We now have [tex]\(25x^2y^{10}\)[/tex] from the first part and [tex]\(y^{12}\)[/tex] from the second part.
- Combine these results: [tex]\(25x^2y^{10} \cdot y^{12}\)[/tex].
- For the [tex]\(y\)[/tex] terms, add the exponents: [tex]\(y^{10} \cdot y^{12} = y^{10+12} = y^{22}\)[/tex].
4. Final Simplified Expression:
- The simplified form of the entire expression is [tex]\(25x^2y^{22}\)[/tex].
Therefore, the correct simplification of the expression is [tex]\(25x^2y^{22}\)[/tex]. The answer is:
[tex]\[
25x^2y^{22}
\][/tex]
1. Simplify the first part [tex]\((5xy^5)^2\)[/tex]:
- The expression [tex]\((5xy^5)^2\)[/tex] is being squared.
- First, square the coefficient: [tex]\(5^2 = 25\)[/tex].
- Next, apply the power of 2 to [tex]\(x\)[/tex]: [tex]\((x)^2 = x^2\)[/tex].
- Finally, apply the power of 2 to [tex]\(y^5\)[/tex]: [tex]\((y^5)^2 = y^{5 \times 2} = y^{10}\)[/tex].
So the result of [tex]\((5xy^5)^2\)[/tex] is [tex]\(25x^2y^{10}\)[/tex].
2. Simplify the second part [tex]\((y^3)^4\)[/tex]:
- Here, apply the power of 4 to [tex]\(y^3\)[/tex]: [tex]\((y^3)^4 = y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the simplified parts:
- We now have [tex]\(25x^2y^{10}\)[/tex] from the first part and [tex]\(y^{12}\)[/tex] from the second part.
- Combine these results: [tex]\(25x^2y^{10} \cdot y^{12}\)[/tex].
- For the [tex]\(y\)[/tex] terms, add the exponents: [tex]\(y^{10} \cdot y^{12} = y^{10+12} = y^{22}\)[/tex].
4. Final Simplified Expression:
- The simplified form of the entire expression is [tex]\(25x^2y^{22}\)[/tex].
Therefore, the correct simplification of the expression is [tex]\(25x^2y^{22}\)[/tex]. The answer is:
[tex]\[
25x^2y^{22}
\][/tex]
