Answer :
To simplify the expression [tex]\(\left(5xy^5\right)^2\left(y^3\right)^4\)[/tex], let's break it down into clear steps:
1. Simplify [tex]\((5x y^5)^2\)[/tex]:
- First, apply the power to each part inside the parentheses.
- [tex]\((5x)^2\)[/tex] becomes [tex]\(5^2 \cdot x^2 = 25x^2\)[/tex].
- [tex]\((y^5)^2\)[/tex] means you multiply the exponents \: [tex]\(y^{5 \times 2} = y^{10}\)[/tex].
- Thus, [tex]\((5xy^5)^2\)[/tex] simplifies to [tex]\(25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- Here, multiply the exponents for [tex]\(y^3\)[/tex] by 4.
- [tex]\(y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the results:
- We now need to multiply the results of the two parts: [tex]\( (25x^2y^{10}) \cdot (y^{12}) \)[/tex].
- Multiply the coefficients and the same base variables separately.
- The coefficient remains [tex]\(25x^2\)[/tex].
- Combine the powers of [tex]\(y\)[/tex]: [tex]\((y^{10}) \cdot (y^{12}) = y^{10+12} = y^{22}\)[/tex].
Therefore, the simplified expression is [tex]\(25x^2y^{22}\)[/tex].
Thus, the correct answer is [tex]\(25x^2y^{22}\)[/tex].
1. Simplify [tex]\((5x y^5)^2\)[/tex]:
- First, apply the power to each part inside the parentheses.
- [tex]\((5x)^2\)[/tex] becomes [tex]\(5^2 \cdot x^2 = 25x^2\)[/tex].
- [tex]\((y^5)^2\)[/tex] means you multiply the exponents \: [tex]\(y^{5 \times 2} = y^{10}\)[/tex].
- Thus, [tex]\((5xy^5)^2\)[/tex] simplifies to [tex]\(25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- Here, multiply the exponents for [tex]\(y^3\)[/tex] by 4.
- [tex]\(y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the results:
- We now need to multiply the results of the two parts: [tex]\( (25x^2y^{10}) \cdot (y^{12}) \)[/tex].
- Multiply the coefficients and the same base variables separately.
- The coefficient remains [tex]\(25x^2\)[/tex].
- Combine the powers of [tex]\(y\)[/tex]: [tex]\((y^{10}) \cdot (y^{12}) = y^{10+12} = y^{22}\)[/tex].
Therefore, the simplified expression is [tex]\(25x^2y^{22}\)[/tex].
Thus, the correct answer is [tex]\(25x^2y^{22}\)[/tex].
