What is x^{1/3}y^{1/3}(x^{1/6}-y^{1/6}) ?

The solution to x^{1/3}y^{1/3}(x^{1/6}-y^{1/6}) is (x^{1/6}-y^{1/6})(xy)^{1/3}

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simplify x^{1/3}y^{1/3}(x^{1/6}-y^{1/6})

simplify

x^{\frac{1}{3}} y^{\frac{1}{3}} (x^{\frac{1}{6}} - y^{\frac{1}{6}})

(x^{\frac{1}{6}} - y^{\frac{1}{6}}) (x y)^{\frac{1}{3}}

Solution steps

x^{\frac{1}{3}} y^{\frac{1}{3}} (x^{\frac{1}{6}} - y^{\frac{1}{6}})

Apply exponent rule:

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

assuming

a \geq 0, b \geq 0

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

= (x^{\frac{1}{6}} - y^{\frac{1}{6}}) (x y)^{\frac{1}{3}}

6.6 \cdot 1 0^{- 28}

(8 x) (24 x^{4} y)

33 (33)

(p)^{11}

What is x^{1/3}y^{1/3}(x^{1/6}-y^{1/6}) ?
The solution to x^{1/3}y^{1/3}(x^{1/6}-y^{1/6}) is (x^{1/6}-y^{1/6})(xy)^{1/3}