Explain how the following equation can be simplified without the use of a calculator.

Question

Explain how    can be simplified without the use of a calculator.

Please be clear and concise as well as detailed. And format your answer neatly. Thank you! :D

Answer 1

256 = 4(64) = 2^2(8^2) = 16^2 = (4^2)^2 = 4^4

(16^2)^(3/4) = (the 4th root of 16^2)^3 = (the square root of 16), raised to the 3rd power

square root of 16 = 4, cubed = 4^3 = 4x4x4 = 4(16 = 64

256^(3/4) = 64

or plug into an online calculator like Desmos to get 64

256^1/2 = 16

256^1 = 16(4)(4) = 4(4)(4)(4) = 256

256^(3/4) = 64= 16(4)= 4(4)(4) which is between 16 and 256

256^x increases by a factor of 4 as x increases by 1/4

x goes from 1/2 to 3/4 to 1, or 2/4 to 3/4 to 4/4, as 256^x goes from 16 to (4)16 to 4(4)(16