Question

(1/3)^7 (1/3)^3 (-1/3)^8

simplify this expression

Answer 1

use 1/x = x^(-1)

Answer 2

so if this was \[a^7 *a^3\] what would that simplify to?

Answer 3

a^10

Answer 4

alright, good, so for yours to start a=1/3

Answer 5

so now for the -1/3

Answer 6

let's think for a moment. Exponents are just shorthand for multiplication, right?

Answer 7

right

Answer 8

so, what's the difference between 5*5 and -5*-5?

Answer 9

no difference, both equals 25

Answer 10

alright, so what about 2*2*2 and -2*-2*-2?

Answer 11

8 and -8

Answer 12

alright, so when you have a negative number to an even power, do you think the answer will be positive or negative?

Answer 13

how about for an odd power?

Answer 14

negative for even and positive for odd

Answer 15

so -5*-5 was negative? that's (-5)^2

Answer 16

no positive...

Answer 17

i dont know where you're going with this lmao

Answer 18

well what's gonna be the difference between \[(1/3)^8~~and~~(-1/3)^8\]

Answer 19

same answer

Answer 20

right, so you said before if you had a^3 * a^7 you get a^(10) well, so now, you said that there is no difference between the positive 1/3 to the eighth and negative 1/3 to the eighth. that means we essentially have a^3*a^7*a^8

Answer 21

which, you can easily simplify :)

Answer 22

1?

Answer 23

how did you get 1?

Answer 24

what's a^(10)*a^8?

Answer 25

i used 1 for a then plugged it into my calculator

Answer 26

a^18

Answer 27

why would you pick an a value? our a is 1/3

Answer 28

and a^18 is correct

Answer 29

so 1/3^18

Answer 30

have to use exponent rules

Answer 31

and yes

Answer 32

thanks for explaining!

Answer 33

np, I hope you get the process

Answer 34

i do understand now! don't multiply the fractions together if they are all the same (: thanks.