What is \sqrt[4]{[x^2+y^4]^2} ?

The solution to \sqrt[4]{[x^2+y^4]^2} is sqrt([x^2+y^4])

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simplify \sqrt[4]{[x^2+y^4]^2}

simplify

[x^{2} + y^{4}]

Solution steps

Apply radical rule:

= ([x^{2} + y^{4}]^{2})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

= [x^{2} + y^{4}]^{2 \cdot \frac{1}{4}}

2 \cdot \frac{1}{4} = \frac{1}{2}

= [x^{2} + y^{4}]^{\frac{1}{2}}

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

= [x^{2} + y^{4}]

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(x + 2)^{2} (x + 3)^{2}

1 6^{x + 1}

What is \sqrt[4]{[x^2+y^4]^2} ?
The solution to \sqrt[4]{[x^2+y^4]^2} is sqrt([x^2+y^4])