# Thread: Changing fractions to a power

1. ## Changing fractions to a power

I am given a fraction, 1/128 and asked to give the answer as a power of 2.

If I divide this number I get 0.00078125, which I am sure is not right.

Powers to me are all about 10^ something, what I am struggling with here is how to turn a fraction into a power?

Thanks

David

2. Hello,

How about$\displaystyle \left(\frac{1}{8\sqrt{2}} \right)^{2}$ ?

3. $\displaystyle 128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^7$

so
$\displaystyle 128=\frac{1}{2^{7}} = 2^{-7}$

What you wrote is correct but is not completely simplified (8, for example, can be written as 2^3. and $\displaystyle \sqrt{2}^2 = 2$)

$\displaystyle \left(\frac{1}{8\sqrt{2}} \right)^{2}$

$\displaystyle = \frac{1^2}{(8\sqrt{2})^2}$

$\displaystyle = \frac{1}{8^2 (\sqrt{2})^2}$

$\displaystyle = \frac{1}{(2^3)^2 \times 2}$

$\displaystyle = \frac{1}{2^6 \times 2}$

$\displaystyle = \frac{1}{2^7}$

$\displaystyle = 2^{-7}$

4. Originally Posted by David Green

I am given a fraction, 1/128 and asked to give the answer as a power of 2.

If I divide this number I get 0.00078125, which I am sure is not right.

Powers to me are all about 10^ something, what I am struggling with here is how to turn a fraction into a power?

Thanks

David
LaTex doesn't appear to be working today. Maybe it is just my reader but I will try tell you what the others are saying.

I think what the others are trying to tell you is that powers can be of any base. In particular, powers of 2 are 2^1= 1, 2^2= 4, 2^3= 8, 2^4= 16, 2^5= 32, 2^6= 64, 2^7= 128. And, of course, negatives put the number into the denominator. So 1/128= 2^?.

5. Originally Posted by David Green

I am given a fraction, 1/128 and asked to give the answer as a power of 2.

If I divide this number I get 0.00078125, which I am sure is not right.

Powers to me are all about 10^ something, what I am struggling with here is how to turn a fraction into a power?