Answer:
[tex]360x^{2}y^{2}z^{3}[/tex]
Step-by-step explanation:
1. You have the following expression given in the problem above:
[tex]12x\sqrt{900x^{2}x^{4}z^{6}}[/tex]
2. To simplify it, multiply all the exponents inside the square root by [tex]\frac{1}{2}[/tex], because [tex]12x\sqrt{900x^{2}x^{4}z^{6}}=12x({900x^{2}x^{4}z^{6}})^{\frac{1}{2}}[/tex]
3. Then, you have:
[tex]900^{\frac{1}{2}}=30\\x^{(2)(\frac{1}{2})}=x\\y^{(4)(\frac{1}{2})}=y^{2}\\z^{(6)(\frac{1}{2})}=z^{3}[/tex]
4. Therefore, the simplified form is:
[tex](12x)(30x)(y^{2})(z^{3})=360x^{2}y^{2}z^{3}[/tex]
