Final answer:
To rewrite the expression 5/2^x + 5/2^(x+3) as A*5/2^x, we combine the terms over a common denominator, resulting in the value of A being 45/8.
Step-by-step explanation:
The given expression is 5/2^x + 5/2^(x+3). To find the value of A so that we can rewrite the expression as A*5/2^x, we need to combine the terms over a common denominator. Since the first term already has a denominator of 2^x, we need to make the denominator of the second term the same. To do this, we can represent 2^(x+3) as 2^x * 2^3, which simplifies to 2^x * 8.
So our second term becomes 5/(2^x * 8) or 5/2^x * 1/8, which simplifies to (5/8)/2^x. Then, we can add the two terms which share the same denominator, giving:
(5/2^x) + ((5/8)/2^x) = (5 + 5/8)/2^x = (40/8 + 5/8)/2^x = (45/8)/2^x
Now, to represent this as A*5/2^x, A will be 45/8 because:
A*5/2^x = (45/8)*5/2^x = (45/8)/2^x
Therefore, the value of A is 45/8.