Question

Simplify this expression: `[(−1/2)^2]^3-:2^-3 ·(−1/2)^-4 -: 2^11 =`? Hint: `[(1/a)^n]^m= (1/a)^(n+m)` `a^j xx a^k = a^(j+k)` this true for all power expression so long they have the same base

Answer 1

`[(-1/2)^2]^3-:2^(-3)*(-1/2)^-4)-:2^11)=1/2^10`

Explanation:

`[(-1/2)^2]^3-:2^(-3)*(-1/2)^-4)-:2^11`

= `(-1*2^(-1))^(2xx3)-:2^(-3)*(-1*2^(-1))^(-4)-:2^11`

= `(-1)^6*(2^(-1))^(2xx3)-:2^(-3)*(-1)^(-4)*2^4-:2^11`

= `1*2^(-6)-:2^(-3)*1*2^4-:2^11`

= `2^(-6)-:2^(-3)*2^4-:2^11`

= `2^(-6-(-3)+4-11)=2^(-10)=1/2^10`