How do you simplify #81^ { 16^ { - 4^ { - 2^-1} } } + ( 4^ { 8} ) ^ { - 3} \cdot ( 4^ { - 6} ) ^ { - 6}#?

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Answer 1 · 2017-07-22T02:33:36

See a solution process below:

We will simplify this expression right to left:

#81^(16^(-4^(-2^-1))) + (4^8)^-3 * color(blue)((4^-6)^-6) =>#

#81^(16^(-4^(-2^-1))) + (4^8)^-3 * color(blue)((4^(-6 * -6)) =>#

#81^(16^(-4^(-2^-1))) + (4^8)^-3 * color(blue)(4^36) =>#

#81^(16^(-4^(-2^-1))) + color(red)((4^8)^-3) * color(blue)(4^36) =>#

#81^(16^(-4^(-2^-1))) + color(red)(4^(8 * -3) * color(blue)(4^36) =>#

#81^(16^(-4^(-2^-1))) + color(red)(4^-24) * color(blue)(4^36) =>#

#81^(16^(-4^(-2^-1))) + color(red)(1/4^24) * color(blue)(4^36) =>#

#81^(16^(-4^(-2^-1))) + color(blue)(4^36)/color(red)(4^24) =>#

#81^(16^(-4^(-2^-1))) + 4^(color(blue)(36)- color(red)(24)) =>#

#81^(16^(-4^(-2^-1))) + 4^12 =>#

#81^(16^(-4^color(red)(-2^-1))) + 4^12 =>#

#81^(16^color(red)(-4^2)) + 4^12 =>#

#81^(16^color(red)(-8)) + 4^12 =>#

#81^-128 + 4^12 =>#

#1/81^128 + 4^12#