How do you simplify ${(\frac{8}{125})}^{\frac{2}{3}}$ $(8/125)^(2/3)$ ?

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Answer 1 · 2017-03-12T15:34:39

$\frac{4}{25}$ $4/25$

${[\frac{8}{125}]}^{\frac{2}{3}} = {[\frac{2 \times 2 \times 2}{5 \times 5 \times 5}]}^{\frac{2}{3}}$ $[8/125]^(2/3) = [(2xx2xx2)/(5xx5xx5)]^(2/3)$

$\Rightarrow {[\frac{2^{1 + 1 + 1}}{5^{1 + 1 + 1}}]}^{\frac{2}{3}}$ $rArr [(2^(1+1+1))/(5^(1+1+1))]^(2/3)$

$\Rightarrow {[\frac{2^{3}}{5^{3}}]}^{\frac{2}{3}}$ $rArr[(2^3)/(5^3)]^(2/3)$

$\Rightarrow {[{(\frac{2}{5})}^{3}]}^{\frac{2}{3}}$ $rArr [(2/5)^3]^(2/3)$

$\Rightarrow {[\frac{2}{5}]}^{2}$ $rArr[2/5]^2$

$\Rightarrow \frac{4}{25}$ $rArr 4/25$

How do you simplify (8/125)^(2/3)(8125)23(8/125)^(2/3)?