Respuesta :
You have the following expression:
[tex]\sqrt[]{40x^4y^3z}[/tex]In order to simplify it you need to remember this property for Radicals:
[tex]\sqrt[n]{a^n}=a^{\frac{n}{n}}=a[/tex]Then:
- Descompose the number 40 into its Prime factors:
[tex]40=2\cdot2\cdot2\cdot5[/tex]- Apply the Product of Powers property that states:
[tex](b^m)(b^n)=b^{(m+n)}[/tex]Then:
[tex]40=2^2\cdot2\cdot5[/tex]- Rewrite the expression:
[tex]=\sqrt[]{2^2\cdot2\cdot5\cdot x^4\cdot y^2\cdot y\cdot z}[/tex]- Simplifying, you get:
[tex]=2x^2y\sqrt[]{2\cdot5yz}=2x^2y\sqrt[]{10yz}[/tex]The answer is:
[tex]2x^2y\sqrt[]{10yz}[/tex]