What is the product of cbrt(9) * sqrt(3) in simplest radical form?

To find the product of ( \sqrt[3]{9} ) and ( \sqrt{3} ) in simplest radical form, we first express both terms using exponents.

The cube root of 9 can be rewritten as:

[

\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{2/3}

]

The square root of 3 can be expressed as:

[

\sqrt{3} = 3^{1/2}

]

Now, we multiply the two expressions together:

[

\sqrt[3]{9} \cdot \sqrt{3} = 3^{2/3} \cdot 3^{1/2}

]

When multiplying like bases, we add the exponents:

[

3^{2/3 + 1/2}

]

To add ( \frac{2}{3} ) and ( \frac{1}{2} ), we need a common denominator. The least common multiple of 3 and 2 is 6, so we convert the fractions:

[

\frac{2}{3} = \frac{4}{6} \quad \text{