which expression is not equal to 125?
a) 5(5^3/2/5)^2
b) (5^3/5^4)^-3
c) 5^-2/5^-5
d) 5(5^5/5^3)
To determine which expression is not equal to 125, we can simplify each expression and see if it equals 125.
a) 5(5^3/2/5)^2
This expression simplifies to 5(5^(3/2)/5)^2 = 5(√5/5)^2 = 5(√5/5)(√5/5) = 5(√5/25) = √5/5
Since √5/5 is not equal to 125, option a is not equal to 125.
b) (5^3/5^4)^-3
This expression simplifies to (5^(3-4))^(-3) = 5^-1^(-3) = 5^3 = 125
Since 125 is equal to 125, option b is equal to 125.
c) 5^-2/5^-5
This expression simplifies to 5^(-2-(-5)) = 5^(3) = 125
Since 125 is equal to 125, option c is equal to 125.
d) 5(5^5/5^3)
This expression simplifies to 5^(5-3) = 5^2 = 25
Since 25 is not equal to 125, option d is not equal to 125.
Therefore, the expression that is not equal to 125 is d) 5(5^5/5^3).