Question

Simplify:

2^a + 2^(a+2) / 2^(a-1)

I can't find anyway to simplify it and get the answer (5/2) unless I sub in a value which isn't really simplifying

Answer 1

(2^a + 2^a * 2^2)/ 2^a/ 2^1
(2^a + 4*2^a)/ 2^a / 2^1
5(2^a) / 2^a /2
10(2^a)/ 2^a
10 <===

Answer 2

x = 2^a
x+4x/[x/2]
10
2^a = 10
\[a = \log_{2}10 \]

Answer 3

\[Given Equation: 2^{a}+2^{a+2}/2^{a-1}\]

-> \[2^{a}(1+2^{2})/2^{a}\times2^{-1}\]

Answer 4

=10

Answer 5

sry...10

Answer 6

But my book says the answer is 5/2 :S

Answer 7

i tried the other way,

2^a / 2^ (a-1) + 2^(a +2)/ 2^(a-1)
2^(a - a +1) + 2^ (a +2 -a +1)
2^1 + 2 ^3 = 2 +8 = 10
it's still coming out the same answer...Unless the book made mistake

Answer 8

I'd say the simplification is \[2^a+8\]
because \[2^a+2^{a+2}/2^{a-1}\]=>\[2^a+2^{a+2-(a-1)}=>2^a+2^{3}=>2^a+8\]

Answer 9

\[\frac{2^a+2^{a+2}}{2^{a-1}}=\frac{2^a(1+2^2)}{2^{a-1}}=2^{a-a+1}(1+2^2)=2\times 5=10\]