Considering the conversion from exponent to radical, the equation that justifies why the expression [tex]9^{\frac{1}{3}} = \sqrt[3]{9}[/tex] is correct is.
[tex](9^{\frac{1}{3}})^{3} = 9^{\frac{3}{3}} = 9[/tex]
The conversion of rational exponents to radical notation is modeled by:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
In this problem, the expression is:
[tex]9^{\frac{1}{3}} = \sqrt[3]{9}[/tex]
And the equation that shows that this is correct is:
[tex](9^{\frac{1}{3}})^{3} = 9^{\frac{3}{3}} = 9[/tex]
More can be learned about the conversion from exponent to radical at https://brainly.com/question/19627260
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