Question

Pls help me answer this question thx

Answer 1

`\large\boxed{(1)/(115)}`

Explanation:

`\text{Use}\\\\(a^n)^m=a^(nm)\\\\a^n\cdot a^m=a^(n+m)\\\\(a\cdot b)^n=a^n\cdot b^n\\\\a^(-1)=(1)/(a)\\--------------------------\\\\(5^(2n-1)-4(25^(n-1)))/((5^n\cdot2)^2+3(5^(2n-1)))=(5^(2n)\cdot5^(-1)-4\left[(5^2)^n\cdot25^(-1)\right])/((5^n)^2\cdot2^2+3\left[(5^2)^n\cdot5^(-1)\right])`

`=(5^(2n)\cdot(1)/(5)-4\left(5^(2n)\cdot(1)/(25)\right))/(5^(2n)\cdot4+3\left(5^(2n)\cdot(1)/(5)\right))=(5^(2n)\left((1)/(5)-(4)/(25)\right))/(5^(2n)\left(4+(3)/(5)\right))=((5)/(25)-(4)/(25))/(4(3)/(5))=(1)/(25):\left((4\cdot5+3)/(5)\right)\\\\=(1)/(25)\cdot(5)/(23)=(1)/(5)\cdot(1)/(23)=(1)/(115)`