Question

explain 5^-2

Answer 1

rules of exponent
\[x^{-n} = \frac{1}{x^n}\]

Answer 2

but why is it .04 instead of .4?

Answer 3

5^{-2} is the multiplicative inverse of 5^2

Answer 4

\[\frac{1}{x^{-n}} = x^n\]

Answer 5

wait what is that ^?

Answer 6

let me show you an example

Answer 7

\[x^{-n} = \frac{1}{x^n} \rightarrow 5^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04\]

Answer 8

ohhhhhhhhhhhhh lol yea i was pretending... I knew that pshhhh

Answer 9

To take it one step further

\[\frac{1}{25} = \frac{4}{100} = 0.04\]

Answer 10

right...

Answer 11

yeah that 4/100 was a necessary step

Answer 12

aren't you going to ask why 4/100 = 0.04 ? @yomamabf

Answer 13

because its in the hundredth decimal place

Answer 14

so let me show you the other one
\[\frac{1}{x^{-n}}= x^n \rightarrow \frac{1}{5^{-2}} = 5^2 = 5 \times 5 = 25 \]

Answer 15

that ones new im gonna take note of that nincompoop

Answer 16

Because

\[\frac{1}{25} \times \frac{4}{4} = \frac{4}{100}\]