How do you simplify ${(\frac{4}{9})}^{\frac{3}{2}}$ $(4/9)^(3/2)$ ?

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How do you simplify ${(\frac{4}{9})}^{\frac{3}{2}}$ $(4/9)^(3/2)$ ?

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Answer 1 · 2017-10-19T14:16:53

$\frac{8}{27}$ $8/27$ = ${(\frac{2}{3})}^{3}$ $(2/3)^3$

Explanation:

${(\frac{4}{9})}^{\frac{3}{2}} = \frac{4^{1} \cdot 4^{\frac{1}{2}}}{9^{1} \cdot 9^{\frac{1}{2}}}$ $(4/9)^(3/2) = (4^1*4^(1/2))/(9^1*9^(1/2)$
$= \frac{4 \cdot \sqrt{4}}{9 \cdot \sqrt{9}}$ $=(4*sqrt4)/(9*sqrt9)$
$= \frac{4 \cdot 2}{9 \cdot 3} = \frac{8}{27}$ $=(4*2)/ (9*3) = 8/27$

Aliter :
${(/ 9)}^{\frac{3}{2}} = {({(\frac{4}{9})}^{\frac{1}{2}})}^{3} = {(\frac{2}{3})}^{3} = \frac{8}{27}$ $(/9)^(3/2) = ((4/9)^(1/2))^3 = (2/3)^3=8/27$

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How do you simplify ${(\frac{4}{9})}^{\frac{3}{2}}$ $(4/9)^(3/2)$ ?

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