What is (x^2+8xy+16y^2)^{1/3}*(x+4y)^{1/3} ?

The solution to (x^2+8xy+16y^2)^{1/3}*(x+4y)^{1/3} is x+4y

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simplify (x^2+8xy+16y^2)^{1/3}*(x+4y)^{1/3}

simplify

(x^{2} + 8 x y + 16 y^{2})^{\frac{1}{3}} \cdot (x + 4 y)^{\frac{1}{3}}

x + 4 y

Solution steps

(x^{2} + 8 x y + 16 y^{2})^{\frac{1}{3}} (x + 4 y)^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0, b \geq 0

(x^{2} + 8 x y + 16 y^{2})^{\frac{1}{3}} (x + 4 y)^{\frac{1}{3}} = ((x^{2} + 8 x y + 16 y^{2}) (x + 4 y))^{\frac{1}{3}}

= ((x^{2} + 8 x y + 16 y^{2}) (x + 4 y))^{\frac{1}{3}}

Factor

(x + 4 y) (x^{2} + 8 x y + 16 y^{2}) : (x + 4 y)^{3}

= ((x + 4 y)^{3})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

= (x + 4 y)^{3 \cdot \frac{1}{3}}

3 \cdot \frac{1}{3} = 1

= x + 4 y

(x^{8} + 2 x^{7} - 3 x^{6} + 2 x^{5} - x^{4}) e n t re (x^{4})

e^{a} \cdot e^{b}

2 x^{2}

45^{2}

What is (x^2+8xy+16y^2)^{1/3}*(x+4y)^{1/3} ?
The solution to (x^2+8xy+16y^2)^{1/3}*(x+4y)^{1/3} is x+4y