Question

Help please
Working on stuff for a class need an answer.

Answer 1

`2a^3(\sqrt[4]{9b^3} )`

Explanation:

Given:

`\sqrt[4]{144a^(12)b^3}`

144 as a product of its prime factors is
`2^4* 3^2`

Now,
`a^(12)` can be written as
`(a^3)^4`
`(\because (a^m)^n=a^(m* n))`

We know that,
`\sqrt[4]{a^4} =a`

Hence, the given expression becomes,

`\sqrt[4]{2^4* 3^2* (a^3)^4* b^3} \\=2a^3(\sqrt[4]{3^2* b^3}\\ =2a^3(\sqrt[4]{9b^3})`