# Question: The 4th Power

## Comment on The 4th Power

### Alright, How do i know I have

Alright, How do i know I have to use 1/4, before using the power of a power rule here.

Thanks ### Our goal is to find the value

Our goal is to find the value of x^4. So, what do we need to do to x^16 (given) to get x^4 (our goal)?
Well, if we raise x^16 to the power of 1/4, we get x^4. Perfect!
So, let's raise both sides of the equation to the power of 1/4 (and then apply the power of a power rule)

Likewise, let's say we know that x^3 = 8, and we want to find the value of x (you probably already know that x will equal the cube root of x, but let's look at it in terms of exponents).
We want to find the value of x (aka x^1)
So, let's take x^3 = 8 and raise both sides to the power of 1/3
We get: (x^3)^(1/3) = 8^(1/3)
Simplify to get: x^1 = 8^(1/3)
In other words, x = the cube root of x

Does that help?

### Off course! You are always

Off course! You are always the savior. Thanks

### WITH INDICES PROBLEMS. I

WITH INDICES PROBLEMS. I THOUGHT I HAD IT ALL FIGURED OUT UNTIL I GOT TO THE QUESTIONS IN THE LAST THREE VIDEOS UNDER POWER AND ROOTS. MY CONFIDENCE JUST HAD A BOOST

### can I also do it like this:

can I also do it like this:
if x^16 = 16, then x^4 will be 4th root of x^16, and then take the 4th root of 16 to get 2? ### Most definitely!

Most definitely!
In fact, the 4th root of x^16 is exactly the same as (x^16)^(1/4)
In general, the kth root of n = n^(1/k)

### I am not sure if this has

I am not sure if this has been explained already by Tsedze or Admin, but this is the way I saw it:
x^16 = (x^4)^4
And
(x^4)^4 = 16
So I asked, what number to the 4th power = 16, which gave the answer, 2. ### Good stuff!

Good stuff!
That's somewhat similar to tsedze's approach, but a little less formal.

### When i see a new problem i

When i see a new problem i get confused and can't decide how to start. ### That's very common.

That's very common.

For this particular question, we're given information about x^16, and we're asked about the value of x^4

So, we need to do SOMETHING to our information about x^16 so that we can make a conclusion about the value of x^4