How do you simplify ${(3^{\frac{1}{2}} \cdot 5^{\frac{2}{3}})}^{\frac{3}{2}}$ $(3^(1/2) * 5^(2/3)) ^(3/2)$ ?

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Answer 1 · 2018-07-25T21:42:17

$5 \cdot 3^{\frac{3}{4}}$ $5\cdot 3^{3/4}$

Given that

${(3^{\frac{1}{2}} \cdot 5^{\frac{2}{3}})}^{\frac{3}{2}}$ $(3^{1/2}\cdot 5^{2/3})^{3/2}$

$= {(3^{\frac{1}{2}})}^{\frac{3}{2}} \cdot {(5^{\frac{2}{3}})}^{\frac{3}{2}}$ $=(3^{1/2})^{3/2}\cdot (5^{2/3})^{3/2}$

$= (3^{\frac{3}{2} \cdot \frac{1}{2}}) \cdot (5^{\frac{3}{2} \cdot \frac{2}{3}})$ $=(3^{3/2\cdot 1/2})\cdot (5^{3/2\cdot 2/3})$

$= (3^{\frac{3}{4}}) \cdot (5)$ $=(3^{3/4})\cdot (5)$

$= 5 \cdot 3^{\frac{3}{4}}$ $=5\cdot 3^{3/4}$

How do you simplify (3^(1/2) * 5^(2/3)) ^(3/2)(312⋅523)32(3^(1/2) * 5^(2/3)) ^(3/2)?