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Popular >

simplify (sqrt(1-x^2))^x

Solution

simplify

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

Solution

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

Solution steps

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

Simplify

\frac{1}{2} x : \frac{x}{2}

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

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

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Frequently Asked Questions (FAQ)

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