Rational Exponents with Negative Coefficients - Problem 1

Simplify an expression with a rational exponent and a negative coefficient. So what we need to deal with here is figure out a; what the 3/2 is telling us and also where this negative sign is in terms of being associated with that power.

So order of operations tells us to do exponents first and which tells me that this negative is not associated with that exponent. So now what we have to do is figure out what 25 to the 3/2 is. I always do the root first, power over roots so that tells me the denominator, this is just going to be negative 25 to the 1/2 to the third with the negative out in front. 25 to the 1/2 is the same thing as the square root of 25, so this is just 5³ with a negative out in front, the negative comes after the exponent so we have -5³. 5³ is 125 leaving us with -125.

So making sure we have our negative in the right spot and then going through our rules of rational exponents, power over root to solve out an equation.