Why does (8/27)^(2/3) = 4/9 ?
When you are solving questions like this, can you always divide the top two fractions and the bottom two fractions to give you your answer?
+118609 $$\left(\frac{8}{27}\right)^{(2/3)}\\\\
=\frac{8^{(2/3)}}{27^{(2/3)}}\\\\
now\\\\
8^{2/3}=\left(8^{1/3}\right)^2=\left(\sqrt[3]{8}\right)^2=2^2=4\\\\
and\\\\
27^{2/3}=\left(27^{1/3}\right)^2=\left(\sqrt[3]{27}\right)^2=3^2=9\\\\
\mbox{So the answer is }\\\\
\dfrac{4}{9}$$
+118609 $$\left(\frac{8}{27}\right)^{(2/3)}\\\\
=\frac{8^{(2/3)}}{27^{(2/3)}}\\\\
now\\\\
8^{2/3}=\left(8^{1/3}\right)^2=\left(\sqrt[3]{8}\right)^2=2^2=4\\\\
and\\\\
27^{2/3}=\left(27^{1/3}\right)^2=\left(\sqrt[3]{27}\right)^2=3^2=9\\\\
\mbox{So the answer is }\\\\
\dfrac{4}{9}$$
