Question

Simplify: ${\left(\frac{x^{-1}{y}^2}{x^2{y}^{-4}}\right)}^7+{\left(\frac{x^{-3}{y}^5}{x^2{y}^{-3}}\right)}^5$

• A. $0$
• B. $-1$
• C. $xy$
• D. $x^{-25}{y}^{40}(x^4{y}^2+1)$

Answer 1

The correct option is D $x^{-25}{y}^{40}(x^4{y}^2+1)$

${\left(\frac{x^{-1}{y}^2}{x^2{y}^{-4}}\right)}^7+{\left(\frac{x^{-3}{y}^5}{x^2{y}^{-3}}\right)}^5={\left(x^{-3}{y}^6\right)}^7+{\left(x^{-5}{y}^8\right)}^5=x^{-21}{y}^{42}+x^{-25}{y}^{40}=x^{-25}{y}^{40}(x^4{y}^2+1)$