need the explanation of steps for 9^1/4/9^3/4

Question

please explain each step i.e., like I know step one is using the quotient rule to subtract exponents then I need to know each step from there to answer of 1/3

 

ok more specifically I need to use the following if applicable: principal root, product rule, quotient rule, recriprocal and nth root

Answer 1

Here are some properties of exponents that you'll need:

1. x^a*x^b = x^a+b
2. 1/x^a = x^-a

 

9^1/4/9^3/4

 

= 9^1/4*9^-3/4       [Property 2]

= 9^1/4-3/4           [Property 1]

= 9^-1/2               [1/4 - 3/4 = -2/4 = -1/2]

= 1/9^1/2             [Property 2]

 

= 1/3               [9^1/2 = (3²)^1/2 = 3]