Question

What value of n solves the equation?
3n = 1 over 81
n =

Answer 1

Divide 3 on both sides.

Answer 2

to get only n.

Answer 3

caz \[\frac{ 3n }{ 3 } = n\]

Answer 4

you should put in an ^ to show it's an exponent
3^n = 1/81

Answer 5

this isnt making any sense to me

Answer 6

the first "trick" is factor 81. can you do that ?

Answer 7

like get the factors of 81?

Answer 8

yes, the prime factors

Answer 9

1, 3, 9, 27, 81

Answer 10

I meant what prime numbers do you multiply together to get 81 ?

for 6, it would be 2*3
for 8 it would be 2*2*2
etc

Answer 11

oh, okay... but how is this in relation to my question? /.\ Sorry imn really confused rn

Answer 12

you will see in a minute

Answer 13

you find them by dividing 81 by the first prime that works: by 3
3*27
then simplify 27, to get 3*3*9 and finally 3*3*3*3

Answer 14

now write 3*3*3*3 in "short-hand" using exponents
can you do that ?

Answer 15

what do you mean by in short hand?

Answer 16

using exponents

Answer 17

people invented exponents to make it easy to write
2*2*2*2 as 2^4

Answer 18

oh okay. Yes... so like 2 to the 4 power. 2 tot eh 4th power is 16... sorry I woke up like 10 minutes ago... and im still tired... oh god cx

Answer 19

2 was an example

so far we know
81 = 3*3*3*3

use exponents to re-write the right-hand side

Answer 20

yes... but how am I supposed to re-write 1 over 81?

Answer 21

one step at a time.

can you write 3*3*3*3 using exponents?

Answer 22

ok, but you can type it as
3^4

in your problem, we can write
\[ 3^n = \frac{1}{81} \\ 3^n = \frac{1}{3^4} \]

ok ?

Answer 23

oh, okay

Answer 24

the problem is as I posted
\[ 3^n = \frac{1}{3^4} \]

However, there is a rule using exponents. you can "flip" a fraction and make the exponent negative. Like this:
\[ 3^n = 3^{-4} \]

Answer 25

now you "match up" 3^n with 3^(-4)
the "n" matches with the -4