How do you simplify fractions with negative exponents?

[Biaach]

Hi I am an 8th grader i got to do my homework lol help me fast please!
How do you do a problem like this??
2 -2
--
3

 

[Biaach]

so what this question is 2 over 3 with a negetive exponent. sorry about that/

 

[symbolipoint]

Your question is not precise. Try either good typesetting or use clear text-based notation; otherwise express clearly in writing what help you want.

How is the exponent applied? Is it applied to the entire fraction or is it applied just to the numerator?

 

[Biaach]

it is only applied in the numerator.
2 over 3 with an negative exponent next to the 2.
How the heck do you do this :(
oh and the negetive exponent is -2.

 

[Integral]

Note that I have moved your post.

Not sure what your number is. Do you mean:

$$({ \frac 2 3 })^{-2}}$$

 

[Biaach]

Note that I have moved your post.

Not sure what your number is. Do you mean:

$$({ \frac 2 3 })^{-2}}$$

YES! THAT IS EXACTLY WHAT I MEAN :)
Can any1 help me with this now? :)

 

[Integral]

Ok so you have:

$$\frac {2^{-2}} 3$$

What do you know about negitive exponents?

 

[Biaach]

Ok so you have:

$$\frac {2^2} 3$$

What do you know about negitive exponents?

I do know that you have to multiply it with the numerator and you get a negetive answer.

so -2 x 2 = -4
and it would be
-4 over 3

 

[Integral]

I do know that you have to multiply it with the numerator and you get a negetive answer.

so -2 x 2 = -4
and it would be
-4 over 3

No, that will not work. So do you understand the meaning of $2^{-1}$?

 

[Biaach]

No, that will not work. So do you understand $2^{-1}$

isnt $2^{-1}$ = -2?

Explain other details please

 

[Integral]

isnt $2^{-1}$ = -2?

Explain other details please

Nope!

$$2^{-1} = \frac 1 2$$

 

[Math Is Hard]

This might help:

http://www.mathsisfun.com/algebra/negative-exponents.html

 

[Elucidus]

Understanding the meaning of 2^-1 is critical to handling any question of this type and your original question in particular.

What does your instructor/notes/text give as the definition of a^-n?

How would you apply that definition to 2^-1?

--Elucidus

 

[Biaach]

Nope!

$$2^{-1} = \frac 1 2$$

How?

 

[Math Is Hard]

How?

Look at the link I posted.

 

[Biaach]

Understanding the meaning of 2^-1 is critical to handling any question of this type and your original question in particular.

What does your instructor/notes/text give as the definition of a^-n?

How would you apply that definition to 2^-1?

--Elucidus

She told me to multiply the numerator with the exponent i think, and the answer would be a negative number

 

[Biaach]

Oh and she said something about Reciprocal

 

[Elucidus]

How?

From the Product Rule of Exponents we want

$$2^1 \cdot 2^{-1} = 2^{1+(-1)} = 2^0 = 1$$.

But 2¹ = 2 so

$$2 \cdot 2^{-1} = 1$$ implies

$$2^{-1} = \frac{1}{2}$$

by dividing both sides by 2.

--Elucidus

 

[Integral]

Don't you have a textbook?

 

[Biaach]

From the Product Rule of Exponents we want

$$2^1 \cdot 2^{-1} = 2^{1+(-1)} = 2^0 = 1$$.

But 2¹ = 2 so

$$2 \cdot 2^{-1} = 1$$ implies

$$2^{-1} = \frac{1}{2}$$

by dividing both sides by 2.

--Elucidus

Can you give an example using the problem i posted?

 

[Elucidus]

She told me to multiply the numerator with the exponent i think, and the answer would be a negative number

What do your notes indicate? Does your text define this?

If it is the case your instructor actually said this, then she is sadly mistaken.

--Elucidus

 

[Elucidus]

Can you give an example using the problem i posted?

The intent is to help you do the problem for yourself, not do it for you even under the pretext as using the original question as an examlpe.

But I can show you a close cousin:

Simplfy $$\frac{2^{-3}}{4^{-1}}$$

$$= \frac {\left(\frac{1}{2^3}\right)}{\left(\frac{1}{4^1}\right)}<br /> = \frac {\left(\frac{1}{8}\right)}{\left(\frac{1}{4}\right)}<br /> =\frac{1}{8} \cdot \frac{4}{1} = \frac{4}{8} = \frac{1}{2}.$$

--Elucidus