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Mathematics
OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

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

OpenStudy (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?

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

sorry i still dont understand..

OpenStudy (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?

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

no it did the same thing

OpenStudy (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?

OpenStudy (anonymous):

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

OpenStudy (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.

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

Hm. What do you mean?

OpenStudy (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.

OpenStudy (shadowfiend):

Sorry, 1 / 8^2 = 1 / 64

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

Exactly.

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

Right! :)

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

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

OpenStudy (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

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

yep i got that

OpenStudy (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?

OpenStudy (anonymous):

256

OpenStudy (shadowfiend):

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

OpenStudy (anonymous):

4?

OpenStudy (shadowfiend):

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

OpenStudy (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?

OpenStudy (anonymous):

64?

OpenStudy (shadowfiend):

Exactly :)

OpenStudy (anonymous):

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

OpenStudy (shadowfiend):

Cool.

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