Question

Question 12
With steps please

Answer 1

`Answer:\ \boxed{5^2}`

`\sqrt[n]{a}=a^(1)/(n)\\\\\text{therefore}\\\\\sqrt5=5^(1)/(2)\\----------------\\25=5^2\\----------------\\78,125=5^7\\----------------\\\text{use}\\\\a^n\cdot a^m=a^(n+m)\\\\(a^n)/(a^m)=a^(n-m)\\----------------\\\\\frac{\sqrt5*78,125}{25*5^{(7)/(2)}}=(5^(1)/(2)*5^7)/(5^2*5^(7)/(2))=\frac{5^{(1)/(2)+7}}{5^{2+3(1)/(2)}}=\frac{5^{7(1)/(2)}}{5^{5(1)/(2)}}=5^{7(1)/(2)-5(1)/(2)}=\boxed{5^2}`