# How do you show that 512^(2/3) = 16^(3/2) by using the properties of exponents?

Apr 7, 2015

${512}^{\frac{2}{3}}$
$= {\left({512}^{\frac{1}{3}}\right)}^{2}$
$= {\left(\sqrt[3]{512}\right)}^{2}$
$= {8}^{2}$
$= 64$

${16}^{\frac{3}{2}}$
$= {\left({16}^{\frac{1}{2}}\right)}^{3}$
$= {\left(\sqrt{16}\right)}^{3}$
$= {4}^{3}$
$= 64$

Therefore
${512}^{\frac{2}{3}} = {16}^{\frac{3}{2}}$