Answer :
Sure! Let's simplify the expression [tex]\((5xy^5)^2(y^3)^4\)[/tex] step-by-step.
1. Simplify [tex]\((5xy^5)^2\)[/tex]:
- When raising a product to a power, you apply the exponent to each part of the product:
- [tex]\((5)^2 = 25\)[/tex]
- [tex]\((x)^2 = x^2\)[/tex]
- [tex]\((y^5)^2 = y^{5 \times 2} = y^{10}\)[/tex]
- So, [tex]\((5xy^5)^2 = 25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- Apply the power to the exponent of [tex]\(y\)[/tex]:
- [tex]\((y^3)^4 = y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the results:
- Now, we need to multiply [tex]\(25x^2y^{10}\)[/tex] by [tex]\(y^{12}\)[/tex].
- For the [tex]\(y\)[/tex] terms, add the exponents: [tex]\(y^{10} \times y^{12} = y^{10+12} = y^{22}\)[/tex].
4. Final expression:
- Combine all parts to write the simplified expression:
- The expression [tex]\((5xy^5)^2(y^3)^4\)[/tex] simplifies to [tex]\(25x^2y^{22}\)[/tex].
So, the correct simplification of the expression is [tex]\(25x^2y^{22}\)[/tex].
1. Simplify [tex]\((5xy^5)^2\)[/tex]:
- When raising a product to a power, you apply the exponent to each part of the product:
- [tex]\((5)^2 = 25\)[/tex]
- [tex]\((x)^2 = x^2\)[/tex]
- [tex]\((y^5)^2 = y^{5 \times 2} = y^{10}\)[/tex]
- So, [tex]\((5xy^5)^2 = 25x^2y^{10}\)[/tex].
2. Simplify [tex]\((y^3)^4\)[/tex]:
- Apply the power to the exponent of [tex]\(y\)[/tex]:
- [tex]\((y^3)^4 = y^{3 \times 4} = y^{12}\)[/tex].
3. Combine the results:
- Now, we need to multiply [tex]\(25x^2y^{10}\)[/tex] by [tex]\(y^{12}\)[/tex].
- For the [tex]\(y\)[/tex] terms, add the exponents: [tex]\(y^{10} \times y^{12} = y^{10+12} = y^{22}\)[/tex].
4. Final expression:
- Combine all parts to write the simplified expression:
- The expression [tex]\((5xy^5)^2(y^3)^4\)[/tex] simplifies to [tex]\(25x^2y^{22}\)[/tex].
So, the correct simplification of the expression is [tex]\(25x^2y^{22}\)[/tex].
