Question 1209835
Let's simplify the expression step-by-step:

**1. Rewrite 25 as 5^2:**

25^(1/2 - log 5 + √3) = (5^2)^(1/2 - log 5 + √3)

**2. Apply the Power of a Power Rule:**

(5^2)^(1/2 - log 5 + √3) = 5^(2 * (1/2 - log 5 + √3))

**3. Distribute the 2:**

5^(2 * (1/2 - log 5 + √3)) = 5^(1 - 2log 5 + 2√3)

**4. Apply the Logarithm Power Rule (2log 5 = log 5^2):**

5^(1 - 2log 5 + 2√3) = 5^(1 - log 5^2 + 2√3) = 5^(1 - log 25 + 2√3)

**5. Separate the Exponents:**

5^(1 - log 25 + 2√3) = 5^1 * 5^(-log 25) * 5^(2√3)

**6. Apply the Logarithm Identity (a^(-log_a(x)) = 1/x):**

Remember that log 25 is log base 10 of 25. We can rewrite 5^(-log 25) using the change of base formula.

* 5^(-log(25)) = 5^(-log(25)/log(10))
* We can rewrite 5^(-log(25)) as 10^(log(5)*(-log(25)/log(10)))
* We can rewrite 5^(-log(25)) as 10^(-log(25)*log(5)/log(10))
* We can rewrite 5^(-log(25)) as 10^(-log(25)*log(5))
* We can rewrite 5^(-log(25)) as 10^(log(25^(-log(5))))
* We can rewrite 5^(-log(25)) as 25^(-log(5))
* We can rewrite 5^(-log(25)) as (5^2)^(-log(5))
* We can rewrite 5^(-log(25)) as 5^(-2log(5))
* We can rewrite 5^(-log(25)) as 5^(log(5^(-2)))
* We can rewrite 5^(-log(25)) as 5^(log(1/25))
* We can rewrite 5^(-log(25)) as 1/25

5^1 * 5^(-log 25) * 5^(2√3) = 5 * (1/25) * 5^(2√3)

**7. Simplify:**

5 * (1/25) * 5^(2√3) = (1/5) * 5^(2√3)

**Final Simplified Form:**

(1/5) * 5^(2√3) or 5^(2√3 - 1)