How do you evaluate #(\frac { 1} { 2} ) ^ { - 1} + ( \frac { 1} { 2} ) ^ { 0} + ( \frac { 1} { 2} ) ^ { 1} #?

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Answer 1 · 2017-09-26T11:50:37

See a solution process below:

First, use this rule of exponents to eliminate the negative exponent on the leftmost term:

#x^color(red)(a) = 1/x^color(red)(-a)#

#(1/2)^color(red)(-1) + (1/2)^0 + (1/2)^1 =>#

#1/(1/2)^color(red)(- -1) + (1/2)^0 + (1/2)^1 =>#

#1/(1/2)^color(red)(1) + (1/2)^0 + (1/2)^1#

Next, use this rule of exponents to simplify the left and right terms in the expression:

#a^color(red)(1) = a#

#1/(1/2)^color(red)(1) + (1/2)^0 + (1/2)^color(red)(1) =>#

#1/(1/2) + (1/2)^0 + (1/2) =>#

#2 + (1/2)^0 + 1/2#

Now, use this rule of exponents to simplify the middle term and then evaluate the expression:

#a^color(red)(0) = 1#

#2 + (1/2)^color(red)(0) + 1/2 =>#

#2 + 1 + 1/2 =>#

#3 1/2# or #3.5#