Question

Express $-\frac{16}{81}$ as power of a rational number.

• A. $-(\frac{4}{9}{)}^2$
• B. $(\frac{4}{9}{)}^2$
  
• C. $(\frac{4}{9}{)}^2$
  
• D. $-(\frac{-4}{9}{)}^2$
  

Answer 1

Answer: (A), (D)

The correct options are
A $-(\frac{4}{9}{)}^2$
D $-(\frac{-4}{9}{)}^2$


$\frac{-16}{81}=\frac{-(4{)}^2}{(9{)}^2}=-{\left(\frac{4}{9}\right)}^2(\because \frac{a^m}{b^m}=(\frac{a}{b}{)}^m)$
Also, $4^2=(-4{)}^2⟹-{\left(\frac{4}{9}\right)}^2=-{\left(\frac{4}{9}\right)}^2$