Question

explain this rule for exponents: x^(-n) = 1/x^n

Answer 1

what does "explain" mean in this context?

Answer 2

if it means "give an example" you can say
\[10^{-2}=\frac{1}{10^2}=\frac{1}{10}=0.01\]

Answer 3

if it means 'why is it true?' the answer would be "it is true by definition"

Answer 4

it says in my own words, explain this rule for exponents

Answer 5

oh okay

Answer 6

then use your own words

Answer 7

^ I was going to say that, but I was afraid it'd be too cheeky ^.^

Answer 8

@PeterPan new around here?

Answer 9

Ten days, or eleven.

Answer 10

the cheek will come take my word for it

Answer 11

I would but I don't understand what they are wanting

Answer 12

@HelenKizer really use your own words
what it says is exactly what it says, that \(x^{-n}=\frac{1}{x^n}\) i.e. to take something to a power that is negative, it means take the reciprocal of that number raised to the positive power

Answer 13

for example
\[2^{-3}=\frac{1}{2^3}=\frac{1}{8}\] or
\[\left(\frac{1}{4}\right)^{-3}=4^3=64\] or
\[\frac{1}{5^{-2}}=5^2=25\]

Answer 14

Thank you !

Answer 15

Or you can sound fancy, and write this down...
\[\huge 1=x^0=x^{n-n}=x^{-n}x^n\]

Answer 16

\[\Huge \frac1{x^n}=x^{n-1}\]

Answer 17

oops

Answer 18

oops? :/

Answer 19

typo there