Simplify: s^-3t^-5/(s^2t^3)^-1

Question

simplify assume that no denominator is equal to zero

Answer 1

The rule that allows for the inversion of the negative exponents is: x^-n = 1/x^n or 1/x^-n = x^n that is how we can rewrite the equation as s^-3t^-5/(s^2t^3)^-1 = [(s^2)(t^3)]^1 / [(s^3)(t^5)] with the ^ it can get a bit confusing...but rewrite the equations but replace the ^ with the appropriate exponents...then you will see it much better. The rule for dividing exponents is: x^n / x^m = x^n-m if an only if the base 'x' is the same numerator and denominator. Now look at your rewritten expression: [(s^2)(t^3)]^1 / [(s^3)(t^5)]

Answer 2

Let's start with the -1 exponent that is in the denominator.  We should move this to the top.  At the same time move the -3 and -5 exponents on top to the bottom.  The equation is flipped.  Rewrite:

(s^2*t^3) / (s^3*t^5)  (now we can simplify b dividing like terms.)

answer:  1 / (s*t^2)  (remember with division, we subtract exponent powers of the bottom from the top.)