Choose the correct simplification of the expression (5xy5)2(y3)4. 25x2y22 10x2y22 25x3y14 10x3y14

Answer:A) [tex]25x^2y^{22}[/tex]Step-by-step explanation:The given expression is [tex](5xy^{5})^2 . (y^3)^4[/tex]Here we have to use exponent rules and simplify the expression.Power rule : [tex](a^m)^n = a^{mn}[/tex]Using the above rule, we can write[tex](5xy^{5} )^2 = 5^2.x^2.y^{5*2}[/tex] = [tex]25.x^2.y^10[/tex]Again using the power rule[tex](y^{3} )^4 = y^12[/tex]Now we have to put together this expression, we get= [tex]25.x^2.y^{10} .y^{12}[/tex]Now we have to use product rule.Product rule: [tex]a^m . a^n = a^{m + n}[/tex]Using this rule, we can simplify further= [tex]25..x^2.y^{10 +12}[/tex]= [tex]25x^2y^{22}[/tex]