Question

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

Answer 1

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

Answer 2

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?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

sorry i still dont understand..

Answer 8

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?

Answer 9

Eh. Sorry about that. \(2^3\) would be \(2 \times 2 \times 2 = 8\).

\(2^{-3}\) would be the same as \(\frac{1}{2^3}\).

Answer 10

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

Answer 11

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

Answer 12

no it did the same thing

Answer 13

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?

Answer 14

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

Answer 15

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.

Answer 16

So for example:

2^-3 = 1 / 2^3
3^-8 = 1 / 3^8
215^-15 = 1 / 215^15
3^-35 = 1 / 3^35

Answer 17

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

Answer 18

Hm. What do you mean?

Answer 19

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.

Answer 20

Sorry, 1 / 8^2 = 1 / 64

Answer 21

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

Answer 22

Exactly.

Answer 23

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

Answer 24

Right! :)

Answer 25

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

Answer 26

The only way to take it back out of fraction form is to raise it to -1.

So 1 / 64 = 64^-1.

Answer 27

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

Answer 28

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

Answer 29

yep i got that

Answer 30

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?

Answer 31

256

Answer 32

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

Answer 33

4?

Answer 34

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

Answer 35

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?

Answer 36

64?

Answer 37

Exactly :)

Answer 38

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

Answer 39

Cool.