How do you simplify $3 x^{\frac{2}{3}} y^{\frac{3}{4}} {(2 x^{\frac{5}{3}} y^{\frac{1}{2}})}^{3}$ $3x^(2/3) y^(3/4) (2x^(5/3) y^(1/2))^3$ ?

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How do you simplify $3 x^{\frac{2}{3}} y^{\frac{3}{4}} {(2 x^{\frac{5}{3}} y^{\frac{1}{2}})}^{3}$ $3x^(2/3) y^(3/4) (2x^(5/3) y^(1/2))^3$ ?

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Answer 1 · 2016-06-01T06:05:40

$3 x^{\frac{2}{3}} y^{\frac{3}{4}} {(2 x^{\frac{5}{3}} y^{\frac{1}{2}})}^{3} = 24 x^{\frac{13}{3}} y^{\frac{9}{4}}$ $3x^(2/3)y^(3/4)(2x^(5/3)y^(1/2))^3=24x^(13/3)y^(9/4)$

Explanation:

$3 x^{\frac{2}{3}} y^{\frac{3}{4}} {(2 x^{\frac{5}{3}} y^{\frac{1}{2}})}^{3}$ $3x^(2/3)y^(3/4)(2x^(5/3)y^(1/2))^3$

= $3 x^{\frac{2}{3}} y^{\frac{3}{4}} (2^{3} {(x^{\frac{5}{3}})}^{3} {(y^{\frac{1}{2}})}^{3})$ $3x^(2/3)y^(3/4)(2^3(x^(5/3))^3(y^(1/2))^3)$

= $3 x^{\frac{2}{3}} y^{\frac{3}{4}} \cdot 8 (x^{\frac{5}{3} \times 3}) (y^{\frac{1}{2} \times 3})$ $3x^(2/3)y^(3/4)*8(x^(5/3xx3))(y^(1/2xx3))$

= $24 x^{\frac{2}{3}} y^{\frac{3}{4}} (x^{5}) (y^{\frac{3}{2}})$ $24x^(2/3)y^(3/4)(x^5)(y^(3/2))$

= $24 x^{\frac{2}{3} + 5} y^{\frac{3}{4} + \frac{3}{2}}$ $24x^(2/3+5)y^(3/4+3/2)$

= $24 x^{\frac{13}{3}} y^{\frac{9}{4}}$ $24x^(13/3)y^(9/4)$

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How do you simplify $3 x^{\frac{2}{3}} y^{\frac{3}{4}} {(2 x^{\frac{5}{3}} y^{\frac{1}{2}})}^{3}$ $3x^(2/3) y^(3/4) (2x^(5/3) y^(1/2))^3$ ?