%5E3.jpeg "(2x^3y^4/3xy)^3")
Simplifying the Expression (2x^3y^4/3xy)^3
This article will walk through the steps of simplifying the expression (2x^3y^4/3xy)^3.
Understanding the Problem
We have a fraction raised to the power of 3. To simplify this, we need to apply the rules of exponents.
Step 1: Simplifying the Inside of the Parentheses
- Divide the coefficients: 2/3 = 2/3
- Divide the x terms: x^3/x = x^(3-1) = x^2
- Divide the y terms: y^4/y = y^(4-1) = y^3
This leaves us with (2/3)x^2y^3.
Step 2: Applying the Exponent
Now we have ((2/3)x^2y^3)^3. To apply the exponent to the entire expression, we need to distribute it to each part:
- (2/3)^3 = 8/27
- (x^2)^3 = x^(2*3) = x^6
- (y^3)^3 = y^(3*3) = y^9
Final Result
Putting it all together, the simplified expression is (8/27)x^6y^9.
Therefore, (2x^3y^4/3xy)^3 = (8/27)x^6y^9.