Simplifying the Expression: 28^x-1/28^x-1-1 3/8^x-1+8/64^x-5*8^x+4
In this article, we will simplify the given expression: 28^x-1/28^x-1-1 3/8^x-1+8/64^x-5*8^x+4.
Step 1: Combine Like Terms
First, let's combine the like terms in the expression:
28^x - 1/28^x - 1 = (2 - 1/2)*8^x - 1 = (4/2 - 1/2)*8^x - 1 = (3/2)*8^x - 1
Now, let's simplify the second part of the expression:
3/8^x - 1 + 8/64^x - 58^x + 4 = 3/8^x - 1 + 8/(8^2)^x - 58^x + 4 = 3/8^x - 1 + 1/8^x - 58^x + 4 = (3 + 1)/8^x - 1 - 58^x + 4 = 4/8^x - 1 - 5*8^x + 4
Step 2: Combine the Two Parts
Now, let's combine the two simplified expressions:
(3/2)8^x - 1 + 4/8^x - 1 - 58^x + 4 = (3/2 - 5)*8^x + (4/8^x) - 2 + 4 = (-7/2)*8^x + 1/2^x - 2 + 4
Final Simplification
Finally, let's simplify the expression further:
(-7/2)*8^x + 1/2^x - 2 + 4 = (-7/2)*8^x + 1/2^x + 2
Therefore, the simplified expression is:
*(-7/2)8^x + 1/2^x + 2
Note that we have combined like terms and simplified the expression to its final form.
