To simplify the given expression:
5^2π₯+1 + 2.5^2π₯-1 / 2.5^2π₯
First, we can rewrite 2.5 as 5/2:
5^2π₯+1 + (5/2)^2π₯-1 / (5/2)^2π₯
Now we can use the properties of exponents to simplify:
(5^(2π₯) * 5^1 + 5^(2π₯) * (5/2)^(-1)) / (5/2)^(2π₯)
(5^(2π₯+1) + 5^(2π₯) * (2/5)^(1)) / (5/2)^(2π₯)
(5^(2π₯+1) + 5^(2π₯) * 2/(5^2)) / (5/2)^(2π₯)
(5^(2π₯+1) + 5^(2π₯) * 2/25) / (5/2)^(2π₯)
Now we can simplify further if needed, but this is the fully simplified form of the expression.
2.1
Simplify fully, without the use of a calculator:
2.1.2
5^2π₯+1+2.5^2π₯β1 /2.5^2π₯
(3)
3 answers
how can you call that final mess "simplified"?
I suspect the question has been mangled, since
(5/2)^2π₯-1 / (5/2)^2π₯ = 5^-1 = 1/5
so the whole thing is just
5^2π₯+1 + 1/5
I doubt this was the original intent
I suspect the question has been mangled, since
(5/2)^2π₯-1 / (5/2)^2π₯ = 5^-1 = 1/5
so the whole thing is just
5^2π₯+1 + 1/5
I doubt this was the original intent
Apologies for the confusion in my previous response. Let me simplify the expression correctly.
Given expression:
(5^2π₯+1 + 2.5^2π₯-1) / 2.5^2π₯
Rewriting the expression with 2.5 as 5/2:
(5^(2π₯+1) + (5/2)^(2π₯-1)) / (5/2)^(2π₯)
Using the property of exponents, we get:
(5^(2π₯) * 5^1 + (5/2)^(2π₯) / (5/2)^(2π₯)
(5^(2π₯) * 5 + (5/2)^(2π₯) / (5/2)^(2π₯)
(25 * 5^2π₯ + (5/2)^(2π₯) / (5/2)^(2π₯)
(25 * 5^2π₯ + 2^(2π₯) * 5^(-2π₯))
(25 * 5^(2π₯) + 1) / 5
25 * 5^(2π₯) / 5 + 1 / 5
5^(2π₯) * 5 + 1 / 5
25 * 5 + 1 / 5
125 + 1 / 5
126 / 5
So, the simplified expression is 126/5. Thank you for catching the error and helping with the correction.
Given expression:
(5^2π₯+1 + 2.5^2π₯-1) / 2.5^2π₯
Rewriting the expression with 2.5 as 5/2:
(5^(2π₯+1) + (5/2)^(2π₯-1)) / (5/2)^(2π₯)
Using the property of exponents, we get:
(5^(2π₯) * 5^1 + (5/2)^(2π₯) / (5/2)^(2π₯)
(5^(2π₯) * 5 + (5/2)^(2π₯) / (5/2)^(2π₯)
(25 * 5^2π₯ + (5/2)^(2π₯) / (5/2)^(2π₯)
(25 * 5^2π₯ + 2^(2π₯) * 5^(-2π₯))
(25 * 5^(2π₯) + 1) / 5
25 * 5^(2π₯) / 5 + 1 / 5
5^(2π₯) * 5 + 1 / 5
25 * 5 + 1 / 5
125 + 1 / 5
126 / 5
So, the simplified expression is 126/5. Thank you for catching the error and helping with the correction.
26 answers