Simplify completely: (25^-1/2)/9^-3/2 + 25^-1/2

Answer 1

Michael,

25^(-1/2)/9^(-3/2) + 25^(-1/2) can be simplified when we remember that exponents change their signs when you change where they are in the fraction. Right now we have 25^(-1/2) in the numerator- but if we put it in the denominator instead, we would switch the sign of the exponent and make it 25^(1/2). Same thing with the 9^(-3/2).

So the first step is to change this whole thing to 9^(3/2)/25^(1/2) + 1/25^(1/2). When we add these two fractions, we end up with (9^(3/2) + 1)/25^(1/2). This would be a lovely time to remember that raising a number to 1/2 is the same as taking the square root of it, and that the square root of 25 is 5. Rewrite this as (9^(3/2) + 1)/5.

Let's start recalling our exponent rules in order to simplify our numerator. 9^(3/2) is equal to the square root of 9³. 9³ = 729. The square root of 729 is 27.

We have (27 + 1)/5, or 28/5.

Please search Exponent Rules on Google images. The first result is my favorite- it very neatly conveys all the exponent rules. I turn to this resource constantly.

Hope this helps! :)