Question

$[(-2)^{-2}]^-^4$
FIND THE VALUE

Answer 1

Answer:

The value of given expression , $[( -2 )^{-2} ]^{-4}$ is $256$ .

Step-by-step explanation:

To find  : the value of given expression

Given : $[( -2 )^{-2} ]^{-4}$

Solution :

• Law of exponent :

1. Power of a power : when there are two exponents for single base we multiply both the exponents. i.e. $\left(a^{m}\right)^{n}=a^{m n}$ .

        for example , let , $a = 2 , m = 3 , n =2$

        $[(-2)^{3} ]^{2} = (-2 )^{6} = 64$

• Therefore , solving $[( -2 )^{-2} ]^{-4}$  by applying above rule , we get ,

         $[( -2 )^{-2} ]^{-4} \\\\= [(-2)]^{(-2)(-4 )} \\\\= (-2)^{8} \\\\= (-2)\times (-2 )\times (-2)\times (-2 ) \times(-2)\times (-2 ) \times(-2)\times (-2 )\\\\= 256$