# Thread: What is 1/64 as a power of 4?

1. ## What is 1/64 as a power of 4?

Hi, can someone please explain how to do this question?

Write the number as a power of 4. What is the value of the index?
I'm not just looking for an answer, as I would very much appreciate knowing how to do it too. I'm not even sure I know what an integer or an index is yet.

2. What is 64 as a power of 4?

3. 64 as a power of 4 is $\displaystyle 4^3$. So is $\displaystyle 4^3$ the answer?

Even if it is, it's still not really explaining the question though.

Thanks.

4. Or another way to ask this, is to what power should 4 be raised to, to have 64?

EDIT: I didn't see you above post.

No, that means that:

$\displaystyle \dfrac{1}{64} = \dfrac{1}{4^3}$

What happens when you have a fraction?

5. Actually it should be $\displaystyle 4^{-3}$.

6. Thanks. But you guys are answering with more questions (and answers). What I really need is an explanation.

7. Perhaps you just need to understand what it means to have a negative exponent.

$\displaystyle x^{-n} = \frac{1}{x^n}$

So $\displaystyle 4^{-3} = \frac{1}{4^3} = \frac{1}{64}$

8. Originally Posted by jebus197
Thanks. But you guys are answering with more questions (and answers). What I really need is an explanation.
Well, what we are trying to do is making you think and understand why such and such things work... because we'll not always be here to answer you or to explain things to you. You'll have to be able to think on your own at some point and evaluate whether or not your thought is correct or not.

9. Yes but what I really need is an explanation. Didn't any of you guys maths tutors explain things to you before asking you to do it?

10. $\displaystyle 4^{-1}=\dfrac{1}{4}$ by definition.

So $\displaystyle 4^{-3}=\dfrac{1}{4^3}=\dfrac{1}{64}$.

$\displaystyle 4^{-n}=\dfrac{1}{4^n}$.

11. That's a bit better. Thanks.

12. Originally Posted by jebus197
That's a bit better. Thanks.
There is an assumption that you know something about index laws (otherwise why are you attempting this question). The point of being asked questions is to try and guide you to the answer yourself, based on what you already know. You were told everything you needed to know, the expectation was that you would attempt then to answer the question rather than maintaining a helpless attitude. Post #2 and then particularly post #7 tell you exactly what is required.

What I'd like to see is if you have actually learned anything from this thread. eg. What is 1/81 as a power of 3?

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# express 1/64 as a power of 4

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