### Question Description

simplify and write variables to represent positive real numbers

1. (a^1/2 b)^1/2 over (ab^1/2)

**so far i have used the "nth" root to multiply using the product rule, then i got 1/2 distributed to (a^1/2)**

## Explanation & Answer

[SQRT(a) * (b)]^1/2 divided by a SQRT (b)

(a ^1/2)^1/2 = (a^1/4 * SQRT (b))/ a SQRT (b)

So (a^1/4 * SQRT (b)/ a SQRT (b)

SQRT (b) on numerator and denominator can be eliminated since they equal 1

= a^1/4 / a^1

When you have the same base but different power, subtract numerator from denominator:

a ^(1/4 - 4/4) = a^(-3/4)

= 1/a^3/4