Answer :
We begin with the expression
[tex]$$
(5xy)^2 (y^5)^4.
$$[/tex]
Step 1. Simplify the first factor. When you square a product, each factor is squared:
[tex]$$
(5xy)^2 = 5^2 \cdot x^2 \cdot y^2 = 25x^2y^2.
$$[/tex]
Step 2. Simplify the second factor. When you raise a power to another power, multiply the exponents:
[tex]$$
(y^5)^4 = y^{5\cdot 4} = y^{20}.
$$[/tex]
Step 3. Multiply the two results. When multiplying like bases, add the exponents:
[tex]$$
25x^2y^2 \cdot y^{20} = 25x^2y^{2+20} = 25x^2y^{22}.
$$[/tex]
Thus, the simplified form of the expression is
[tex]$$
25x^2y^{22}.
$$[/tex]
Among the given choices, the correct answer is 25 [tex]$x^2y^{22}$[/tex], which corresponds to option 1.
[tex]$$
(5xy)^2 (y^5)^4.
$$[/tex]
Step 1. Simplify the first factor. When you square a product, each factor is squared:
[tex]$$
(5xy)^2 = 5^2 \cdot x^2 \cdot y^2 = 25x^2y^2.
$$[/tex]
Step 2. Simplify the second factor. When you raise a power to another power, multiply the exponents:
[tex]$$
(y^5)^4 = y^{5\cdot 4} = y^{20}.
$$[/tex]
Step 3. Multiply the two results. When multiplying like bases, add the exponents:
[tex]$$
25x^2y^2 \cdot y^{20} = 25x^2y^{2+20} = 25x^2y^{22}.
$$[/tex]
Thus, the simplified form of the expression is
[tex]$$
25x^2y^{22}.
$$[/tex]
Among the given choices, the correct answer is 25 [tex]$x^2y^{22}$[/tex], which corresponds to option 1.
