%5E6%3Da%5Exb%5Ey.jpeg "(a^3b^4/a^2b)^6=a^xb^y")
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