Question

Simplify:

`[(64)^-2]^-3÷[{(-8)^2}^3]^2`

Answer 1

`[(64)^-2]^-3÷[{(-8)^2}^3]^2`

= `(2^6)^(-2xx-3) ÷ (-8)^(2xx3xx2)`

= `2^(6xx(6)) ÷ (-8)^12`

= `2^(+36)÷(-8)^12`

= `2^(+36)÷[(-2)^3]^12`

= `2^36÷(-2)^36`

= `2^36/(-2)^36`

= `2^36/2^36`    ...(∵36 is even)

= `2^(36-36)`

= 2⁰    ...(∵ a⁰ = 1)

= 1