Question

What number goes in the box?
2 ^ ( ) = (2^7 ÷ 2^9)^3

Answer 1

`x=-6`

Explanation:

`((2^(7))/(2^(9)))^(3) \\((128)/(512))^(3) \\((1)/(4))^(3)\\((1)/(4))*((1)/(4))*((1)/(4))\\(1*1*1)/(4*4*4) \\(1^(3) )/(4^(3) ) \\(1)/(64) \\2^(x)=(1)/(64)\\log 2^x=log(1)/(64)\\x*(log(2))=log(1)/(64)\\x=(log(1)/(64))/(log(2)) \\x=-6`