Question

My question got deleted :/ 4^-2x*4^x= 64 & 6^-2x*6^-x=1/216

Answer 1

HI!!

Answer 2

let's hope there is no rude interruption this time!

Answer 3

\[4^{-2x}\times 4^x=64\] first step is to add the exponents and get \[4^{-x}=64\]

Answer 4

next write \(64\) as \(4^3\) and get \[\huge 4^{-x}=4^3\]
you good from there?

Answer 5

do I just dived 4 on both sides? then it turns to x=-3?

Answer 6

lol no you don't "divide" but you do get \(x=-3\)
it is because if the bases are the same, so are the exponents

Answer 7

\[b^x=b^y\iff x=y\]

Answer 8

so
\[4^{-x}=4^3\iff -x=3\]

Answer 9

next one is almost identical
you want to try it?

Answer 10

Oh, alright. thank you. and yes, for the next one do I turn 1/216 into 216^1?

Answer 11

no
write it as a power of 6

Answer 12

So far I have 6^-x=1/216

Answer 13

6^-x=6^3