\sqrt[3]{27x {}^(15)y {}^(72) }Simply using absolute values as necessary

Question

`\sqrt[3]{27x {}^(15)y {}^(72) }`Simply using absolute values as necessary

Answer 1

one way to see this kind of problems is knowing that:

`\sqrt[3]{x}^2=x^{(2)/(3)}^{}`

so, using sqrt properties

`\sqrt[3]{27\cdot x^(15)\cdot y^(72)}=\sqrt[3]{27}\cdot\sqrt[3]{x^(15)}\cdot\sqrt[3]{y^(72)}`
`\sqrt[3]{27}\cdot\sqrt[3]{x^(15)}\cdot\sqrt[3]{y^(72)}=3\cdot x^{(15)/(3)}\cdot y^{(72)/(3)}`
`3\cdot x^{(15)/(3)}\cdot y^{(72)/(3)}=3\cdot x^5\cdot y^(24)`

So the answer is=

`3\cdot x^5\cdot y^(24)`