How does (sqrt 2)^17 = 256 * sqrt 2
Simplify the following:
(sqrt(2))^17
Multiply exponents. (sqrt(2))^17 = 2^(17/2):
2^(17/2)
2^(17/2) = 2^(16/2+1/2) = 2^(16/2)×sqrt(2):
2^(16/2) sqrt(2)
16/2 = (2×8)/2 = 8:
2^8 sqrt(2)
2^8 = (2^4)^2 = ((2^2)^2)^2:
((2^2)^2)^2 sqrt(2)
2^2 = 4:
(4^2)^2 sqrt(2)
4^2 = 16:
16^2 sqrt(2)
Answer: |256 sqrt(2)
