Question

Find the simplified product: 3sqrt9x^4 x 3sqrt3x^8

Answer 1

`\sqrt[3]{9\text{x}^4} *\sqrt[3]{3\text{x}^8}`

To simplify it we multiply all the terms inside the cube root

`\sqrt[3]{9\text{x}^4} *\sqrt[3]{3\text{x}^8}`

`\sqrt[3]{9\text{x}^4*{3\text{x}^8}}`

Now we apply exponential property

`\text{a}^\text{m}*\text{a}^\text{m}=\text{a}^\text{mn}`

`\text{x}^4*\text{x}^8=\text{x}^(12)`

`\sqrt[3]{9\text{x}^4*{3\text{x}^8}}`

`\sqrt[3]{27\text{x}^(12)}`

Now we take cube root

`\sqrt[3]{27}=3`

`\sqrt[3]{\text{x}^(12)}=\sqrt[3]{\text{x}^3*\text{x}^3*\text{x}^3*\text{x}^3}=\text{x}^4`

`\sqrt[3]{27\text{x}^(12)}`

Answer:

`\rightarrow\boxed{\bold{3x^4}}`