Question

The value of $(243{)}^{-\frac{2}{5}}$ is _______.

• A. $9$
• B. $\frac{1}{9}$
• C. $\frac{1}{3}$
• D. $0$

Answer 1

The correct option is B $\frac{1}{9}$

$(243{)}^{-\frac{2}{5}}=(3^5{)}^{-\frac{2}{5}}=\left(3{)}^{-2}\right[(a^b{)}^m=a^{bm}]=\frac{1}{3^2}=\frac{1}{9}$
The value of $(243{)}^{-\frac{2}{5}}$ is $\frac{1}{9}.$