High School

Choose the correct simplification of the expression [tex]\left(5 x y^5\right)^2\left(y^3\right)^4[/tex].

A. [tex]25 x^2 y^{22}[/tex]
B. [tex]10 x^2 y^{22}[/tex]
C. [tex]25 x^3 y^{14}[/tex]
D. [tex]10 x^3 y^{14}[/tex]

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]