What is (8x^4y^5)^{2/3} ?

The solution to (8x^4y^5)^{2/3} is 4x^{8/3}y^{10/3}

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simplify (8x^4y^5)^{2/3}

simplify

(8 x^{4} y^{5})^{\frac{2}{3}}

4 x^{\frac{8}{3}} y^{\frac{10}{3}}

Solution steps

(8 x^{4} y^{5})^{\frac{2}{3}}

Apply exponent rule:

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

(8 x^{4} y^{5})^{\frac{2}{3}} = 8^{\frac{2}{3}} (x^{4})^{\frac{2}{3}} (y^{5})^{\frac{2}{3}}

= 8^{\frac{2}{3}} (x^{4})^{\frac{2}{3}} (y^{5})^{\frac{2}{3}}

8^{\frac{2}{3}} = 4

= 4 (x^{4})^{\frac{2}{3}} (y^{5})^{\frac{2}{3}}

Simplify

(x^{4})^{\frac{2}{3}} : x^{\frac{8}{3}}

= 4 x^{\frac{8}{3}} (y^{5})^{\frac{2}{3}}

Simplify

(y^{5})^{\frac{2}{3}} : y^{\frac{10}{3}}

= 4 x^{\frac{8}{3}} y^{\frac{10}{3}}

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