What is (x^2-sqrt(1-x^2))^4(x^2+sqrt(1-x^2))^4 ?

The solution to (x^2-sqrt(1-x^2))^4(x^2+sqrt(1-x^2))^4 is (x^2-sqrt(-x^2+1))^4(x^2+sqrt(-x^2+1))^4

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simplify (x^2-sqrt(1-x^2))^4(x^2+sqrt(1-x^2))^4

simplify

(x^{2} - 1 - x^{2})^{4} (x^{2} + 1 - x^{2})^{4}

(x^{2} - - x^{2} + 1)^{4} (x^{2} + - x^{2} + 1)^{4}

Solution steps

(x^{2} - 1 - x^{2})^{4} (x^{2} + 1 - x^{2})^{4}

Apply exponent rule:

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

assuming

a \geq 0, b \geq 0

(x^{2} - - x^{2} + 1)^{4} (x^{2} + - x^{2} + 1)^{4} = ((x^{2} - - x^{2} + 1) (x^{2} + - x^{2} + 1))^{4}

= ((x^{2} - - x^{2} + 1) (x^{2} + - x^{2} + 1))^{4}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= (x^{2} - - x^{2} + 1)^{4} (x^{2} + - x^{2} + 1)^{4}

(x x) (3 x x)

2.05 \cdot 70 0^{- 0.18}

2 e^{- 2 (l n (2))}

What is (x^2-sqrt(1-x^2))^4(x^2+sqrt(1-x^2))^4 ?
The solution to (x^2-sqrt(1-x^2))^4(x^2+sqrt(1-x^2))^4 is (x^2-sqrt(-x^2+1))^4(x^2+sqrt(-x^2+1))^4