anonymous
  • anonymous
simplify (-2)^-5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Psymon
  • Psymon
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.
Psymon
  • Psymon
Forgot the negative on the 2, I apologize.
anonymous
  • anonymous
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

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Psymon
  • Psymon
\[(-2)^{-5}=\frac{ 1 }{ (-2)^{5} } \]
Psymon
  • Psymon
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.
anonymous
  • anonymous
it would be -32 I think?????
Psymon
  • Psymon
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.
Psymon
  • Psymon
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.
anonymous
  • anonymous
So would it be -1/32
Psymon
  • Psymon
Yep.
anonymous
  • anonymous
thank you sooo much and thank you for not giving me just the answer
Psymon
  • Psymon
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?
anonymous
  • anonymous
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
Psymon
  • Psymon
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?
anonymous
  • anonymous
All the 2 are negative in both
Psymon
  • Psymon
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.
anonymous
  • anonymous
i have no idea i would say because its in ( )
Psymon
  • Psymon
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.
anonymous
  • anonymous
i am writing that down so that i wont forget
Psymon
  • Psymon
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?
anonymous
  • anonymous
kinda
Psymon
  • Psymon
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.
anonymous
  • anonymous
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
Psymon
  • Psymon
I really dont mind, lol. Take what ya want to take from this, no copyright xD Now you had the problem: \[\frac{ 1 }{ a ^{-2} }\]?
anonymous
  • anonymous
A^2
Psymon
  • Psymon
Bingo :3
anonymous
  • anonymous
thank you you ROCK!!!!!!!!!
Psymon
  • Psymon
Yeah, glad to help ^_^ Sorry for delay in response, but glad ya got it :3

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