Question

Simplify:${\left(\frac{{2x}^3{y}^2}{{3x}^2{y}^5}\right)}^4\times \left(\frac{x^2{y}^2}{12}\right)$

Answer 1

Let $a={\left(\frac{{2x}^3{y}^2}{{3x}^2{y}^5}\right)}^4\times \left(\frac{x^2{y}^2}{12}\right)$

$=\frac{16x^{12}{y}^8}{81x^8{y}^{20}}\times \frac{x^2{y}^2}{12}$ (since ${\left(a^m\right)}^n=a^{mn})$

$=\frac{16}{81\times 12}\times x^{12+2-8}\times y^{8+2-20}$

$=\frac{4}{81\times 3}\times x^6{y}^{-10}$

$a=\frac{4x^6}{243y^{10}}$

${\left(\frac{{2x}^3{y}^2}{{3x}^2{y}^5}\right)}^4\times \left(\frac{x^2{y}^2}{12}\right)=\frac{4x^6}{243y^{10}}$