## Simplifying Exponential Expressions: (a^3b^4/a^2b)^6 = a^xb^y

This problem involves simplifying an expression with exponents and understanding the rules of exponents. Let's break down the steps:

### Step 1: Simplify the expression inside the parentheses.

**Recall the rule:**a^m / a^n = a^(m-n)- Apply this rule to the variables 'a' and 'b':
- a^3 / a^2 = a^(3-2) = a^1 = a
- b^4 / b = b^(4-1) = b^3

Now the expression becomes: (a b^3)^6

### Step 2: Apply the power of a power rule.

**Recall the rule:**(a^m)^n = a^(m*n)- Apply this rule to both 'a' and 'b':
- (a^1)^6 = a^(1*6) = a^6
- (b^3)^6 = b^(3*6) = b^18

Therefore, the simplified expression is: **a^6 b^18**

### Step 3: Determine the values of x and y

By comparing the simplified expression to a^xb^y, we can see:

**x = 6****y = 18**

Therefore, (a^3b^4/a^2b)^6 = **a^6b^18**