Step-by-step explanation:
1st way
[tex]\sqrt[3]{8}\times \sqrt[3]{8} = \sqrt{16}[/tex]
[tex]8^{\frac{1}{3}}\times 8^{\frac{1}{3}} =16^{\frac{1}{2}}[/tex]
[tex]8^{\left ( \frac{1}{3}+\frac{1}{3} \right )} =16^{\frac{1}{2}}[/tex]
[tex]8^{\frac{2}{3}} =16^{\frac{1}{2}}[/tex]
4 = 4
Hence proved
2nd way
[tex]\sqrt[3]{8}\times \sqrt[3]{8} = \sqrt{16}[/tex]
[tex]\sqrt[3]{8}\times \sqrt[3]{8} = \sqrt{4^{2}}[/tex]
[tex]8^{\frac{1}{3}}\times 8^{\frac{1}{3}} = 4^{\frac{2}{2}}[/tex]
[tex]8^{\frac{2}{3}} = 4^{\frac{2}{2}}[/tex]
[tex]8^{\frac{2}{3}} = 4[/tex]
4 = 4
Hence proved
