if x is a ositive integer, 4x to the one hafl power is equivalent to?
It is equal to twice the square root of the postive integer.
To find the value of 4x to the one-half power, you need to take the square root of 4x. Here's how you can do it step by step:
1. Start with the expression 4x.
2. Take the square root of 4x. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 4x is √(4x).
3. Simplify the square root of 4, which is 2, and multiply it by the square root of x. Therefore, √(4x) = 2√x.
4. Multiply the result by 1/2 to raise it to the power of one-half. Therefore, (2√x)^(1/2) = 2^(1/2) * (√x)^(1/2).
5. Simplify 2^(1/2) to its square root, which is √2. Rewrite (√x)^(1/2) as √√x or the square root of the square root of x.
6. Finally, combine the two results: 2^(1/2) * (√x)^(1/2) = √2 * √√x = √2 * √(√x) = √2 * √(√x) = √2 * (√x)^(1/2) = √2 * √x.
Therefore, 4x to the one-half power is equivalent to √2 * √x or twice the square root of the positive integer x.