simplify (25x^2)^1/2( one over two)
hmm.. i think it will be 5x
Something to the 1/2 power is like taking the square root. As Chopsticks indicated the square root of 25x^2 = 5x.
I hope this helps a little more. Thanks for asking.
To simplify the expression (25x^2)^(1/2)^(1/2), we follow the order of operations, which is the following:
1. Exponents (Powers and Roots)
2. Multiplication and Division (from left to right)
3. Addition and Subtraction (from left to right)
Let's simplify step by step:
Step 1: Simplify the exponent of (25x^2)^(1/2).
To simplify a fractional exponent, we can use the property that (a^m)^n = a^(m * n).
In this case, applying the property, we have:
(25x^2)^(1/2) = 25^(1/2) * (x^2)^(1/2)
Step 2: Simplify the square root of 25.
The square root of 25 is 5, because 5 * 5 = 25.
So, 25^(1/2) = 5.
Step 3: Simplify the square root of (x^2).
The square root of x^2 is simply x, because x * x = x^2.
So, (x^2)^(1/2) = x.
Step 4: Multiply the simplified terms.
Putting everything together, we have:
(25x^2)^(1/2) = 5 * x = 5x
Therefore, the simplified expression is 5x.