Answer: [tex]\frac{2a\sqrt{c}}{3}[/tex]
Step-by-step explanation:
Remember that:
- [tex]\sqrt[n]{a^n}=a[/tex]
- [tex]\sqrt{ab}=(\sqrt{a})(\sqrt{b})[/tex]
- [tex](\sqrt{a})^2=a[/tex]
- The product of powers property establishes that: [tex](a^m)(a^n)=a^{(m+n)}[/tex]
Given the expression [tex]\frac{6(\sqrt{a^3b^2c^4})}{9b\sqrt{ac^3} }[/tex]
You know that:
[tex]a^3=a^2*a\\c^3=c^2*c[/tex]
Then, you must rewrite the expression and simplify:
[tex]\frac{6\sqrt{a^2ab^2c^4}}{9b\sqrt{ac^2c} }=\frac{6abc^2\sqrt{a}}{9bc\sqrt{ac}}=\frac{2ac\sqrt{a}}{3(\sqrt{a})(\sqrt{c})}=\frac{2ac}{3\sqrt{c}}[/tex]
Multiply the numerator and the denominator by [tex]\sqrt{c}[/tex]:
[tex]\frac{(2ac)\sqrt{c})}{(3\sqrt{c})(\sqrt{c})}=\frac{2ac\sqrt{c}}{3(\sqrt{c})^2}=\frac{2ac\sqrt{c}}{3c}=\frac{2a\sqrt{c}}{3}[/tex]
