Why does 1/25 = 2^-5 ?

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Why does 1/25 = 2^-5 ?

Mathematics
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and can you explain this rule to me?
because 2 is raised to a negative power.
that doesn't really help ..

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Other answers:

thats one of the exponent rules. read your book or use google!
a negative exponent is the reciprocal of the positive so x^-2 = 1/(x^2) = 1/5 and 5^-2 = 1/25
^-----This
yea it a rule, learn it, live it, love it!
thank you very much
You will see it again when learning derivatives!
just try to have fun with it!
i can't. math is the death of me :(
no, it just patterns and rules. Like a language.
wait! wouldn't it equal 5^ -2?
5^ -2 = 1/5^2 = 1/25
is that a yes..
yes
so if the rule was 1/a^m = a^ -m......a and m can switch basically?
let me be clear x^-b = 1/(x^b), yes?
so like 1/25 = 1/5^2 = 5^-2 WHICH IS ALSO 2^ -5 so the "a" and "m" switched
yes...
but am i right...what i said?
clear now? Thats the rule, among many :)
please respond to what i said before...
about a and m switching ?? lemme look at it.
can the two values switch like that....like 5^ -2 = 2^ -5
am i right to say that
wait what?
"1/25 = 1/5^2 = 5^-2 WHICH IS ALSO 2^ -5 " this is not true 2^-5 = 1/( 2^5) = 1/32- I misstyped.
okay. do u mind giving me a few of these to practice...like quizzing me i guess lol
sure 3^-3
ummm oh god
lets see..
1/3^3
ugh im wrong
so far so good- and what is 1/(3^3)?
that would be 3^-3
yes, thats true too but what is 3^3?
27
so 1/(3^3) = 1/27 right?
can u give me one where a and m are different numbers
2^-3
okay so this would be 1/2^3
so 1/8
:-)
yes! so you seem to understand.
can u do one with very big numbers? well like somewhere in the 200s-300s?
sure 222^-300
uh oh.... umm lemme think
1/222^300
okay i think i got this now ! just gotta memorize that rule! :D
are you gonna be online bc i might have more questions :)
you might want a calculator at this point, The rule x^-n = 1/(x^n) is true for ALL number
I will be around until Im not :)
we are not allowed to use calculators on our quiz :(
yea so 222^-300 might not be on the quiz :P btw the answer is : 1/80517880668393229147886068496149401306972582290411328168978510994785579115588583551827976204875447471474879862267202705113127441091878902354853813041890222152198455342144439084242078428238138714265508683035791505554760104867426467157715278054403172295031898472730484002817659144331717312161700756934610875579137993642195693033512692240606656314618045823043091894260503678798685779973005364739112564184555335918720320643432850355542239025011335644126445607944039212224942030284232383674702362906793619267527992062005620717473752544451951685766644998888627609736993334783701457851056538472011058453524224265800042617872532780902329250444294802910839828000675334422137717517355426310014485465179583860965376
study hard.
oh my goodness. are you like a math teacher or something. you are so good at this stuff
no, Im a student, like you.
lol i am a junior in high school and i still do not understand this stuff
practice, practice, practice.
ugh. i hate math so much. do you know much about logs
some what is the deal?
hold on give me a minute
you should open another question- there a lot of smart people here.
okay i will. thank you for all your help! hope to talk to you more sometime on the webbiste! :) - Olivia
sure, I will keep an eye out for your questions :)

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