Which if the following is the simplified form of 2^(1-n)*(sqrt 8)^n/  (sqrt 2)^(-n). Options: 1. 2^n  2. 2^(-n)  3. 2^(n-1)  4. 2^(n+1)

Expert Answers

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The following expression has to be simplified: 2^(1 - n)*(sqrt 8)^n)/(sqrt 2)^-n

2^(1 - n)*(sqrt 8)^n)/(sqrt 2)^-n

=> 2^(1 - n)*(2^(3/2)^n)/(2^(-n/2))

=> 2^(1 - n)*(2^(3n/2)/(2^(-n/2))

=> 2^(1 - n)*(2^(3n/2 + n/2)

=> 2^(1 - n)*(2^(2n))

=> 2^1*2^(2n - n)

=> 2^1*2^n

=> 2^(1+n)

The required result is option 4: 2^(n+1)

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