Question

Simplify the following:

`(3x^4y^2(2xy)^5)/((2x^3y^3)^2`

Answer 1

Given: `(3x^4y^2(2xy)^5)/((2x^3y^3)^2`

Step-wise calculation:

1. Expand the powers inside the parentheses:

(2xy)⁵ = 2⁵ × x⁵ × y⁵

(2xy)⁵ = 32x⁵y⁵

(2x³y³)² = 2² × (x³)² × (y³)²

(2x³y³)² = 4x⁶y⁶ 

2. Substitute these back:

`(3x^4y^2 xx 32x^5y^5)/(4x^6y^6) = (3 xx 32 xx x^(4 + 5) xx y^(2 + 5))/(4 xx x^6 xx y^6)`

`(3x^4y^2 xx 32x^5y^5)/(4x^6y^6) = (96x^9y^7)/(4x^6y^6)`

3. Simplify the coefficients and subtract exponents of like bases:

`96/4 = 24`

x^{9 – 6} = x³

y^{7 – 6} = y¹

y^{7 – 6} = y

Thus, 24x³y.