Question

Can somebody explain step by step ?

Answer 1

`3m\sqrt[5]{2m^4p^4}`

Explanation:

We want to find the fifth root of
`486m^9p^4`. In order to do so, we need to factorise

Let's factorise 486 first:

486 = 2 * 243 = 2 *
`3^5`

Ah, we see that
`3^5` can be taken out and becomes 3 outside of the 5th root since the 5th root of

Now look at the variables. We see that since we have p^"4", whose exponent is less than 5, it's impossible for us to write it as a power of 5, so we leave this in the root.

We also have m^"9", which can be written as m^"5" * m^"4". Again, we see that the m^"4" term will have to remain inside the root, but we can take out the m^"5", which becomes m.

Our final answer is thus:
`3m\sqrt[5]{2m^4p^4}`.

~ an aesthetics lover