What is 1/64 as a power of 4?

**jebus197** · December 13th 2010, 06:04 AM

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?
Give your answer as an integer.

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.

**Plato** · December 13th 2010, 06:05 AM

What is 64 as a power of 4?

**jebus197** · December 13th 2010, 06:16 AM

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

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

Thanks.

**Unknown008** · December 13th 2010, 06:19 AM

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:

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

What happens when you have a fraction?

**Plato** · December 13th 2010, 06:31 AM

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

**jebus197** · December 13th 2010, 09:08 AM

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

**snowtea** · December 13th 2010, 09:10 AM

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

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

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

**Unknown008** · December 13th 2010, 09:16 AM

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.

**jebus197** · December 13th 2010, 09:21 AM

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?

**Plato** · December 13th 2010, 09:30 AM

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

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

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

**jebus197** · December 13th 2010, 10:31 AM

That's a bit better. Thanks.

**mr fantastic** · December 13th 2010, 05:32 PM

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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