Three to what power equals 1/387420489

Question

janu16 · Answer

is tht 1 over 387420489

booklover40 · Answer

Yes.

janu16 · Answer

do you have chocies

booklover40 · Answer

No. I solved a bit of the question, but I need help with this part.

janu16 · Answer

can you post the question instead?

janu16 · Answer

i was wondering like what type of question is that lol

booklover40 · Answer

Okay. Hang on...

booklover40 · Answer

Three to what power is equal to (-27)^-6?

booklover40 · Answer

This is for my pre-algebra class.

janu16 · Answer

when you solve (-27)^-6 you get 1 over 387420489 so the question is what power to 3 gets that? hmm

booklover40 · Answer

ya

janu16 · Answer

alright le me think lol

janu16 · Answer

(-27)^(-6)=3^x
(27)^(-6)•(-1)^(-6)=3^x
(27)^(-6)•(1/(-1)^(6))=3^x
(27)^(-6)•(1/1)=3^x
(27)^(-6)=3^x
(3^3)^(-6)=3^x
(3)^(-6•3)=3^x

booklover40 · Answer

All I know is that the exponent is going to be negative. I have a hard time with negative exponents. :(

phi · Answer

this is a problem where you do not expand to get that huge number (making the problem very hard to figure out)

they want you to use "rules of exponents"  (i.e. tricks!)

janu16 · Answer

@booklover40 thats what i came up with

booklover40 · Answer

Thanks!

janu16 · Answer

yw

booklover40 · Answer

It was right! Thank you so much!

anonymous · Answer

$$\frac{1}{3^n}=\frac{1}{387420489} $$n = 18