Question

Express ${16}^{-2}$ as a power with the base 2.

• A. $2^{-8}$
• B. $2^8$
• C. $2^{16}$
• D. $2^{-16}$

Answer 1

The correct option is A $2^{-8}$

$\because 2\times 2\times 2\times 2=16=2^4\therefore {16}^{-2}=(2^4{)}^{-2}=(2{)}^{4\times (-2)}=\left(2{)}^{-8}\right(\because (a^m{)}^n=a^{mn})$