Question

simplify (-2)^-5

Answer 1

When you have a negative exponent, whatever the exponent is being applied to can be flipped upside down. Flipping it upside down makes the exponent positive. For your example, this is what happens:
\[(-2)^{-5}=\frac{ 1 }{ 2^{5} } \]See, all I did was just flip it and then the exponent became positive.

Answer 2

Forgot the negative on the 2, I apologize.

Answer 3

I got 32 is that right. and does that apply always im doing a test and there is like 14 questions like the one I just posted

Answer 4

\[(-2)^{-5}=\frac{ 1 }{ (-2)^{5} } \]

Answer 5

Well notice we have a fraction. Your answer would have to be less than 1, just looking at it visually. 2^5 is 32, but we have (-2)^5, which is different. Andalso keep in mindit is in the denominator.

Answer 6

it would be -32 I think?????

Answer 7

As for flipping to make the exponent positive, absolutely:

\[\frac{ 1 }{ (2x)^{-2} }=(2x)^{2}\]
\[\frac{ x ^{3}y ^{-4} }{ x ^{-2}y }=\frac{ (x ^{3})(x ^{2}) }{ (y)(y ^{4}) }\]Whichever I flip, thesign of theexponent changes.

Answer 8

And you have a fraction. You have:
\[\frac{ 1 }{ (-2)^{5} }\]You have to have a fraction answer. You can do (-2)^5, but its in a denominator of a fraction, you cant decide to just forget the numerator.

Answer 9

So would it be -1/32

Answer 10

Yep.

Answer 11

thank you sooo much and thank you for not giving me just the answer

Answer 12

Yeah, sure :3 Last thing, though. DO you understand why (-2)^5 is negative? Or why (-2)^37 would be negative as well? Were you taught how to tell negative or positive?

Answer 13

not really but i am kinda getting thia next problem i think i got do you mind seeing if its right 1/a^-2 answer -a^2

Answer 14

Well let's explain that now. So:
\[(-2)^{-3}, (-2)^{-9}, (-2)^{89}, (-2)^{17}, (-2)^{33} \]these answers are all negative.
\[(-2)^{6}, (-2)^{18}, (-2)^{1082}, (-2)^{12}, (-2)^{80} \]these answers are all positive. Do you notice anything about the powers that result in negative and what they have in common. And do you notice what all the positive answer powers have in common?

Answer 15

All the 2 are negative in both

Answer 16

No, look at the exponents. The top row are all negative answers. But this is because all the exponents have something in common. Same withthe bottom row. Theyre all positive answers because the exponents have something in common.

Answer 17

i have no idea i would say because its in ( )

Answer 18

Okay, no worries. All the exponents in the top row are odd numbers and all the exponents in the bottom row are even numbers. 1/(-2)^5 wasa negative answer because the exponent was an odd number.

Answer 19

i am writing that down so that i wont forget

Answer 20

Absolutely : ) No matter how large or small the number. If I see the exponent is even, I know the answer is positive. If I see the exponent is odd, I know its negative. Now one thing to be careful about, though.

\[(-2)^{4} = 16\]
\[-2^{4}= -16\]
Now asI just said, if its an even power the answer is positive. But we have to be veru careful about something like this. See how important the parenthesis are?

Answer 21

kinda

Answer 22

Right. Well recall that when we have something like -(x+4), that there is really an invisble 1 there. (-1)(x+4). Think of it like that with this:
\[-2^{4}=(-1)(2)^{4}\] Because of order of operations, this says we do exponents first and then multiply by the negative. But with parenthesis:
\[(-2)^{4}=(1)(-2)^{4} \]This time the negative is ALSO being raised to the 4th power. In the first one it was 2 raised to the 4th then multiplied by a negative. SO this is the difference. The power in the first problem is NOT applied to the negative. In this bottom one it IS applied to the negative.

Answer 23

if its okay i would like to print out our posts that way i can refer to them because the way that you are explaining is so much better than my teacher or a book

Answer 24

I really dont mind, lol. Take what ya want to take from this, no copyright xD Now you had the problem:
\[\frac{ 1 }{ a ^{-2} }\]?

Answer 25

A^2

Answer 26

Bingo :3

Answer 27

thank you you ROCK!!!!!!!!!

Answer 28

Yeah, glad to help ^_^ Sorry for delay in response, but glad ya got it :3