Question

Simplify the following:

`((xy^3)^2(3x^2y)^4)/(xy)^3`

Answer 1

Given expression: `((xy^3)^2(3x^2y)^4)/(xy)^3`

Step-wise calculation:

1. Expand the powers inside the parentheses:

(xy³)² = x²y⁶ 

(3x²y)⁴ = 3⁴(x²)⁴y⁴

(3x²y)⁴ = 81x⁸y⁴ 

(xy)³ = x³y³

2. Substitute these back into the expression:

`(x^2y^6 xx 81x^8y^4)/(x^3y^3) = (81x^(2 + 8)y^(6 + 4))/(x^3y^3)`

`(x^2y^6 xx 81x^8y^4)/(x^3y^3) = (81x^10y^10)/(x^3y^3)`

3. Apply the quotient rule for exponents:

`81x^(10 - 3)y^(10 - 3) = 81x^7y^7`