Answer:
Option b. 4*(a^4)/(b)
Step-by-step explanation:
We have sqrt(16(a^8)(b^-2)).
We know that sqrt(a*b)=sqrt(a)*sqrt(b).
Applying this rule we have:
sqrt(16(a^8)(b^-2)) = sqrt(16)*sqrt((a^8)(b^-2)) = 4sqrt((a^8)(b^-2))
Also we know that:
sqrt(a/b) = sqrt(a)/sqrt(b)
Applying this rule we have:
4sqrt((a^8)(b^-2)) = 4sqrt(a^8)/sqrt(b^-2)
Also we know that
sqrt(a^b) = a^(b/2)
Applying this rule we have:
4*(a^8/2)*(b^-2/2) = 4*(a^4)(b^-1)
Last but no least, we know that:
a^-b = 1/(a^b)
Applying this rule we have:
4*(a^4)(b^-1) = 4*(a^4)/(b)
