Question

How do you simplify `(sqrt(144x))^6`?

Answer 1

`(sqrt(144x))^6=2985984x^3`

Explanation:

We can rewrite square roots as powers of `1/2`:
`(sqrt(144x))^6=((144x)^(1/2))^6`

Now we can use the following exponent rule:
`(a^n)^m=a^(mn)`

`therefore ((144x)^(1/2))^6=(144x)^(6/2)=(144x)^3`

Now we can use another exponent rule:
`(ab)^n=a^nb^n`

`therefore (144x)^3=144^3*x^3=2985984x^3`