What is (1-x)^{1/2}(x)^{1/2} ?

The solution to (1-x)^{1/2}(x)^{1/2} is (x(-x+1))^{1/2}

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simplify (1-x)^{1/2}(x)^{1/2}

simplify

(1 - x)^{\frac{1}{2}} (x)^{\frac{1}{2}}

(x (- x + 1))^{\frac{1}{2}}

Solution steps

(1 - x)^{\frac{1}{2}} (x)^{\frac{1}{2}}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

x^{\frac{1}{2}} (- x + 1)^{\frac{1}{2}} = (x (- x + 1))^{\frac{1}{2}}

= (x (- x + 1))^{\frac{1}{2}}

20 e^{- 2 x} \cdot 80 e^{- 2 x}

49900 \cdot e^{- 300000}

4.91 \cdot 1 0^{- 9}

- 2 (0.5)^{- 3}

28271.59 (1 + 0.065)^{- 3}

What is (1-x)^{1/2}(x)^{1/2} ?
The solution to (1-x)^{1/2}(x)^{1/2} is (x(-x+1))^{1/2}