Question

Simplify
(2 ^ (n + 4) - 6 * 2 ^ (n + 1))/(2 ^ (2(n + 1)))

Answer 1

• 
  `2^(-n)\ or\ 1/2^n`

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Simplify the given expression in below steps:

• 
  `(2^(n+4)-6*2^(n+1))/2^(2(n+1))=`

• 
  `(2^((n+1)+3)-6*2^(n+1))/2^(2(n+1))=`

• 
  `(2^3*2^(n+1)-6*2^(n+1))/2^(2(n+1))=`

• 
  `(8*2^(n+1)-6*2^(n+1))/2^(2(n+1))=`

• 
  `(8-6)*2^(n+1)/2^(2(n+1))=`

• 
  `2*2^(n+1)/2^(2n+2)=`

• 
  `2^(n+2)/2^(2n+2)=`

• 
  `2^(n+2-2n-2)=`

• 
  `2^(-n)\ or\ 1/2^n`

Used exponent rules:

• Product rule,
• Quotient rule,
• Negative exponent rule.