Respuesta :
Given the following expression:
[tex]\sqrt[]{45}(x^{2}y^{3})[/tex]You can simplify it following the procedure shown below:
1. You need to descompose the Radicand (the number 45 inside the radical symbol into its Prime Factors:
[tex]45=3\cdot3\cdot5[/tex]Remember that the Product of powers property states that:
[tex](b^m)(b^n)=b^{(m+n)}[/tex]Then:
[tex]45=3\cdot3\cdot5=3^2\cdot5[/tex]2. Rewrite the expression:
[tex]=\sqrt[]{(3^2\cdot5)}(x^2y^3)[/tex]3. Remember the following property for Radicals:
[tex]\sqrt[n]{a^n}=a[/tex]Then, simplifying, you get that the answer is:
[tex]\begin{gathered} =3\sqrt[]{(5)}x^2y^3 \\ \end{gathered}[/tex]