First, change 9 into exponential form. 9 equals 3 squared. We change 9 into smaller number to find the simplest form of the radical later.
[tex]9^{\frac{2}{3}}[/tex]
[tex]=(3^{2})^{\frac{2}{3}}[/tex]
[tex]=3^{\frac{4}{3}}[/tex]
Second, change into radical form
The denominator of fractional exponent is the root of the radical
[tex]3^{\frac{4}{3}}[/tex]
[tex]= \sqrt[3]{ 3^{4}}[/tex]
Third, simplify the exponential form under the radical using exponential property
[tex]= \sqrt[3]{ 3^{3+1}}[/tex]
[tex]= \sqrt[3]{3^{3} \times 3^{1}}[/tex]
[tex]= \sqrt[3]{3^{3}} \times \sqrt[3]{3} [/tex]
[tex]= 3 \times \sqrt[3]{3} [/tex]
[tex]= 3 \sqrt[3]{3} [/tex]
In the simplest radical form, what remains under the radical is 3
