Indices - Confusing wording of questions

Hi guys,

there are a few questions on my worksheet i have to do for homework that I do not get (i dont get what the question is trying to say)

the first question is:

1. Write to the power of 2

a) √2 b) 1/√2

2. Write as a faction

a) (1/2)^{3} b) 2^{-3}

does anyone know what the answers would be?

thanks

dan

Re: Indices - Confusing wording of questions

Quote:

Originally Posted by

**MaddieMoodle** (i dont get what the question is trying to say)

...

does anyone know what the answers would be?

Hmm, so do you need a clarification on the questions so that you could solve them yourself, or do you need the answers? I am not sure that giving you straight answers is the best thing because you need to understand the theory behind them, and for this you need to read the textbook and probably some examples of solved questions like these. For instance, if you don't know how to write √2 as a power of 2, you just need to read the theory; there is nothing more to this question.

Re: Indices - Confusing wording of questions

i am guessing the answer to 1a would be √2^2? which would then be 4? is this right?

Re: Indices - Confusing wording of questions

if not can you please explain how you would get to the answer... thanks

Re: Indices - Confusing wording of questions

Quote:

Originally Posted by

**MaddieMoodle** i am guessing the answer to 1a would be √2^2? which would then be 4?

No, the question asks to write $\displaystyle \sqrt{2}$ as $\displaystyle 2^x$ for some expression x. This is what it means to write as a power of 2. I am not sure whether √2^2 means $\displaystyle \sqrt{2^2}$ or $\displaystyle \left(\sqrt{2}\right)^2$, but neither of those expressions have the form $\displaystyle 2^x$.

Besides, $\displaystyle \sqrt{2}\approx1.414$ (because $\displaystyle 1.414^2\approx 1.999$) and 1.414 is certainly not 4.

In plain text, you can write sqrt(2^2) to denote $\displaystyle \sqrt{2^2}$ and (sqrt(2))^2 to denote $\displaystyle \left(\sqrt{2}\right)^2$.

Re: Indices - Confusing wording of questions

well i know the formula for ^{n}(sqrt(X)^{m})

and it is: X^{m/n}

But think i get it now.

For a) √2 would the answer be 2^{1/2}??

Re: Indices - Confusing wording of questions

Quote:

Originally Posted by

**MaddieMoodle** if not can you please explain how you would get to the answer... thanks

Studying mathematics consists of two activities: reading theory and solving problems. The latter activity only makes sense when you have learned the corresponding theory and have seen some examples of solved problems. The relationship between $\displaystyle \sqrt{2}$ and $\displaystyle 2^{1/2}}$ is a part of theory, and the fact that you are having difficulty with it tells me that you need to go over the theory again. Now, it would be inefficient to explain theory on this forum. Not only there are many sites that already do this better, but the primary source for theory should generally be textbooks.

For example, you can read about roots and exponents here (especially the last page) and here (especially the last page).

Re: Indices - Confusing wording of questions

Quote:

Originally Posted by

**MaddieMoodle** well i know the formula for ^{n}(sqrt(X)^{m})

and it is: X^{m/n}

But think i get it now.

For a) √2 would the answer be 2^{1/2}??

Yes, this is correct.

Re: Indices - Confusing wording of questions

and then for b) 1/sqrt(2) the answer would be 2^-1/2?

Re: Indices - Confusing wording of questions

Quote:

Originally Posted by

**MaddieMoodle** and then for b) 1/sqrt(2) the answer would be 2^-1/2?

Yes. I would write it 2^(-1/2) to distinguish it from $\displaystyle \frac{2^{-1}}{2}$ (recall that exponentiation is done before division).

Problem 2 asks you to write expressions as $\displaystyle \frac{x}{y}$ for some x and y.

Re: Indices - Confusing wording of questions

i think i worked out 2a to be 1/8 and 2b to be (1/2)^3

this correct?

Re: Indices - Confusing wording of questions

Quote:

Originally Posted by

**MaddieMoodle** i think i worked out 2a to be 1/8 and 2b to be (1/2)^3

2a is correct, but (1/2)^3 is not in the form x / y. In fact the answers to 2a and 2b are the same.

Re: Indices - Confusing wording of questions

Does problem 1 say "to the power of 2" or "**as** a power of 2"?

Re: Indices - Confusing wording of questions

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