How do you simplify #256^ { b + 2} = 4^ { 2- 2b}#?

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Answer 1 · 2017-03-30T05:10:05

#b=-1#

As #256# and #4# both are powers of #2#, we can write #256^((b+2))=4^((2-2b))# as

#(2^8)^((b+2))=(2^2)^((2-2b))#

or #2^(8(b+2))=2^(2(2-2b))#

Hence #8(b+2)=2(2-2b)#

i.e. #8b+16=4-4b#

or #8b+4b=4-16#

or #12b=-12#

i.e. #b=-1#