How do you simplify $64 {(x^{4} y^{3})}^{\frac{5}{6}}$ $64(x^{4}y^{3})^{\frac{5}{6}}$ ?

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How do you simplify $64 {(x^{4} y^{3})}^{\frac{5}{6}}$ $64(x^{4}y^{3})^{\frac{5}{6}}$ ?

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Answer 1 · 2017-06-23T12:48:43

$64 {(x^{4} y^{3})}^{\frac{5}{6}} = 64 x^{3} y^{2} \sqrt[3]{x} \sqrt{y}$ $64(x^4y^3)^(5/6)=64x^3y^2root(3)xsqrty$

Explanation:

Remember ${(a b)}^{m} = a^{m} b^{m}$ $(ab)^m=a^mb^m$ and ${(a^{m})}^{n} = a^{m n}$ $(a^m)^n=a^(mn)$

Hence $64 {(x^{4} y^{3})}^{\frac{5}{6}}$ $64(x^4y^3)^(5/6)$

= $64 \times {(x^{4})}^{\frac{5}{6}} \times {(y^{3})}^{\frac{5}{6}}$ $64xx(x^4)^(5/6)xx(y^3)^(5/6)$

= $64 \times x^{4 \times \frac{5}{6}} \times y^{3 \times \frac{5}{6}}$ $64xx x^(4xx5/6)xxy^(3xx5/6)$

= $64 \times x^{\frac{20}{6}} \times y^{\frac{15}{6}}$ $64xx x^(20/6)xxy^(15/6)$

= $64 \times x^{\frac{2 \times 10}{2 \times 3}} \times y^{\frac{3 \times 5}{3 \times 2}}$ $64xx x^((color(red)2xx10)/(color(red)2xx3))xxy^((color(red)3xx5)/(color(red)3xx2))$

= $64 \times x^{\frac{10}{3}} \times y^{\frac{5}{2}}$ $64xx x^(10/3)xxy^(5/2)$

= $64 \times x^{3 + \frac{1}{3}} \times y^{2 + \frac{1}{2}}$ $64xx x^(3+1/3)xxy^(2+1/2)$

= $64 \times x^{3} x^{\frac{1}{3}} y^{2} y^{\frac{1}{2}}$ $64xx x^3x^(1/3)y^2y^(1/2)$

= $64 x^{3} y^{2} \sqrt[3]{x} \sqrt{y}$ $64x^3y^2root(3)xsqrty$

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How do you simplify $64 {(x^{4} y^{3})}^{\frac{5}{6}}$ $64(x^{4}y^{3})^{\frac{5}{6}}$ ?

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