Question

How do i simplify this as much as possible

6(√a³b²c⁴)/9b√ac³

Answer 1

Answer:
`(2a√(c))/(3)`

Explanation:

Remember that:

• 
  `\sqrt[n]{a^n}=a`
• 
  `√(ab)=(√(a))(√(b))`
• 
  `(√(a))^2=a`
• The product of powers property establishes that:
  `(a^m)(a^n)=a^((m+n))`

Given the expression
`(6(√(a^3b^2c^4)))/(9b√(ac^3) )`

You know that:

`a^3=a^2*a\\c^3=c^2*c`

Then, you must rewrite the expression and simplify:

`(6√(a^2ab^2c^4))/(9b√(ac^2c) )=(6abc^2√(a))/(9bc√(ac))=(2ac√(a))/(3(√(a))(√(c)))=(2ac)/(3√(c))`

Multiply the numerator and the denominator by
`√(c)`:

`((2ac)√(c)))/((3√(c))(√(c)))=(2ac√(c))/(3(√(c))^2)=(2ac√(c))/(3c)=(2a√(c))/(3)`