Question

Simplify 3^-9/3^-12

Answer 1

\[\frac{a^{-b}}{a^{-c}}=a^{c-b}\]
here you have
\[\frac{3^{-9}}{3^{-12}}=?\]
Can you try ?

Answer 2

um.. i dont get what i have to do though... because there are negative exponenets

Answer 3

Okay, I'll explain with an example
When a no. is in denominator, we can bring it to numerator raised to a power of -1 here

\[\frac{4^{-2}}{4^{-3}}=4^{-2}\times (4^{-3})^{-1}\]
\[4^{-2}\times 4^{3}\]
\[4^{-2+3}=4^1\]
Do you get this?

Answer 4

but how can you raise it up by -1?

Answer 5

i get the rest just not that

Answer 6

I'm bringing it to the numerator, that's why it is raised to a power of -1
\[\frac{1}{a}=a^{-1}\]

Answer 7

so i can do the same with 3^-9 x (3^-12)+^-1

Answer 8

yeah, works for any no.

Answer 9

ok then it would be 3^-9+ 13 = 3^4?

Answer 10

or would it still be 3^3?

Answer 11

\[3^{-9}\times 3^{+12}=3^{-9+12}\]

Answer 12

oh ok :)