how do i simplify an expression
8 with a negative 2 exponent

- anonymous

how do i simplify an expression
8 with a negative 2 exponent

- schrodinger

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- shadowfiend

Hm. Depends on what you mean by simplifying, but I assume you want it as a fraction.

- shadowfiend

So a negative exponent means that the number should be in the denominator with a positive exponent. In this case:
\[8^{-2} = \frac{1}{8^2} = \frac{1}{64}\]
Is that enough?

- anonymous

i'm still looking..im not sure if it has to be in a fraction

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- shadowfiend

Sounds good. Let me know when you find out :)

- anonymous

my daughter does not know if simplifying means fraction..all the problem says is simplify each expression

- shadowfiend

I *believe* this should be enough then. It seems like a reasonable assumption that this would be a `simplified' form of \(8^{-2}\).

- anonymous

sorry i still dont understand..

- shadowfiend

Ok, so if you raise a number to a negative exponent, the way to make the exponent positive is to put it in the denominator.
For example, \(\frac{2^3}\) is \(2 \times 2 \times 2 = 8\). \(\frac{2^{-3}\) is the same as \(\frac{1}{2^3}\), which would be \(\frac{1}{8}\). Does that make sense?

- shadowfiend

Eh. Sorry about that. \(2^3\) would be \(2 \times 2 \times 2 = 8\).
\(2^{-3}\) would be the same as \(\frac{1}{2^3}\).

- anonymous

the example ur typing is giving me math processing error..i cant see what ur typing for some reason

- shadowfiend

Yeah, the first one was a mistake. You should see the second post I followed it with.

- anonymous

no it did the same thing

- shadowfiend

Hm. Ok, I'll skip the equations then.
2^3 means 2 with an exponent of 3.
So 2^3 = 2 * 2 * 2 = 4 * 2 = 8.
2^-3 is the same as 1 / 2^3, so the same as 1 / 8. Does that make sense?

- anonymous

ok i'm tryng to understand..im still not gettin it

- shadowfiend

So this is actually the definition of a negative exponent. If I raise a number to a negative exponent, it's the same as dividing one by the number to the positive exponent.

- shadowfiend

So for example:
2^-3 = 1 / 2^3
3^-8 = 1 / 3^8
215^-15 = 1 / 215^15
3^-35 = 1 / 3^35

- anonymous

this is harder than i thought...is the example the answer broken down?

- shadowfiend

Hm. What do you mean?

- shadowfiend

No, those are just different examples of negative exponents. They aren't related to the problem except in showing what a negative exponent means.
In the case for the problem, it is 8^-2. So, if we follow the pattern above, we have:
8^-2 = 1 / 8^2
You can find 8^2 = 8 x 8 = 64.
And the result is 1 / 8^2 = 64.

- shadowfiend

Sorry, 1 / 8^2 = 1 / 64

- anonymous

ok i think i got it..it turns to a fraction?

- shadowfiend

Exactly.

- anonymous

ok so lemme make sure i got this..for the next problem its..2^-5 would it turn into 1/32?

- shadowfiend

Right! :)

- anonymous

ok so i got that part..how do i change it back from the fraction?

- shadowfiend

The only way to take it back out of fraction form is to raise it to -1.
So 1 / 64 = 64^-1.

- anonymous

thanks..i think i understand better now..
ok i have another one..simply each expression give the answer as a fraction or whole number..example; 4^4/4 how can i do this

- shadowfiend

Ok, so 4^4 is the same as 4 x 4 x 4 x 4, right?

- anonymous

yep i got that

- shadowfiend

Right, so what you have is:
(4 x 4 x 4 x 4) / 4
Now, let's back up for a second. What is 4 x 4 / 4?

- anonymous

256

- shadowfiend

Not quite. 4 x 4 is 16. If you divide 16 / 4, what do you get?

- anonymous

4?

- shadowfiend

Exactly. So dividing by 4 cancels one of the multiplications.

- shadowfiend

If we go back to our original problem, (4 x 4 x 4 x 4) / 4, and we cancel out one of the multiplications, what are we left with?

- anonymous

64?

- shadowfiend

Exactly :)

- anonymous

ok thanks..i think i got this one too..i have more..but i wanna finish these problems first

- shadowfiend

Cool.

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