Trying this problem again?

Question

some misunderstood it

Simplify and combine like radicals

5^4 √256x + 5^4 √81x assume that the x represents a positive number

I have to choose from

35^4√x

none of these

15^4√x

20^4√x
Additional Details


the 4 is the exponent in both

Sorry if I had miss wrote it, I am still in the early stages of learning this and not for sure on some stuff

Answer 1

There are a couple of possibilities. On the face of it you have written
5^4 √(256x) + 5^4 √(81x)
= 5^4 (√(256x) + √(81x))
= 5^4 (16√x + 9√x)
= 5^4 (25 √x)
= 5^6 √x
which is none of the supplied answers.

On the other hand, it's possible that what you actually want is

5 (4th√ 256x) + 5 (4th√ 81x)
where I'm using 4th√ to represent the fourth root, i.e. a √ sign with a little 4 above the left hand side.
In this case we get
5 (4th√ (2^8 . x) + 4th√ (3^4 . x))
= 5 (4 . 4th√x + 3 . 4th√ x)
= 5 . 7 . 4th√x
= 35 . 4th√x.

In this case the notation and terminology you have used is very misleading and inappropriate. Note that in this case 4 is NOT an exponent and should certainly not be written as 5^4 √256x (for example), because the 4 is nothing to do with the 5 - it modifies the √ sign.

Answer 2

2+2=4

Answer 3

5^4 √256x + 5^4 √81x =
5^4(16√x + 9√x) =
5^4*25√x =
5^6√x
so the answer is none of these.

Answer 4

5^4 √256x + 5^4 √81x
=5^4 *16x + 5^4 *9x
=5^6 x

Answer 5

I'll go with none of these. The various coefficients can be simplified to
16 x 5^4sqrt(x) + 9 x 5^4sqrt(x) or 25 x 5^4 sqrt(x)
Since 25= 5^2, this becomes 5^6 sqrt(x).