Question

simplify 1/x-1

I think the answer is 1 but i need explanation why please

Answer 1

so is it (1/x) -1 or 1/(x-1)

Answer 2

oh wait its actually 1/(x^-1) my bad.

Answer 3

oh ok. so why do you think it is 1?

Answer 4

Well theres a rule for it i think for example 6^3 in a rational it'll be 1/(6^3) which itll eventually be 1/216 i think that applies to this problem too right?

Answer 5

Well, lets think about a simpler example. Do you know what 2^-1 would be?

Answer 6

1/2 right?

Answer 7

right.

Answer 8

so what about 1 / 2^-1

Answer 9

1 / -2 but since its in the denominator its already considered a negative number i believe.

Answer 10

its not negative 1/2

Answer 11

There is no exponent that will make a number become negative

Answer 12

and a number being in the denominator doesn't mean its negative either

Answer 13

Ohh alright i understand that, although this specific property confuses me a lot.

Answer 14

yeah it can do that

Answer 15

so 1 / 2^-1 would be 1 / 1 / 2

Answer 16

and one divided by one half is two

Answer 17

So it's 2?

Answer 18

so when you have a negative exponent in the denominator, you are basically just moving it back to the numerator.

Answer 19

just like when you have a negative exponent in the numerator, you move it to the denominator

Answer 20

yes its 2

Answer 21

Hmm but the question then asks my why x^1/3 * x^1/3 * x^1/3 is the same as that question. The answer for that one would be x^3/3 which would equal 1 right?

Answer 22

(x ^ (1/3)) * (x ^ (1/3)) * (x ^ (1/3)) = x

Answer 23

when you multiply some base number exponents, so long as the base in the same you add the exponents

Answer 24

so you're just adding (1/3)+(1/3)+(1/3) = 1. But x^1 = x, not 1.

Answer 25

Well yeah i meant that but then how is that the same as the previous one?

Answer 26

Because the answer is the same.

Answer 27

They're both equal x

Answer 28

1/x^-1 = x

Answer 29

Ohhhh they're equal to x?

Answer 30

right

Answer 31

ahh may i ask you the other two then?

Answer 32

ok

Answer 33

Its an add on to the question. This one is 11√x^5*x^4*x^2, i put that it turns out to be 11√x^11 which will then make it 11/11=x which is 1=x

Answer 34

right. The 11th root will undo the 11th exponent leaving only x.

Answer 35

So I'm right?

Answer 36

yes

Answer 37

Awesome and now the last one is 3√x^3 which i put that it'll make 3/3 which is also equal to x.

Answer 38

thats right

Answer 39

Awesome. There's a really confusing one here that has to do with the previous one. If you don't mind that'll be my last one?

Answer 40

Ok lets see

Answer 41

Simplify 1/(3√x-6) I put that it would make 1/(-6/3) which it will make it be 1/-2 = -1 i stopped there.

Answer 42

Ok, so what you want to do here is multiply both the top and bottom by something that will get rid of the radical in the denominator

Answer 43

we have the 3rd root of x-6

Answer 44

or (x-6)^(1/3)

Answer 45

oh man sorry its actually x^-6

Answer 46

I always forget the exponent sign. sorry

Answer 47

oh ok

Answer 48

So
1/
\[\sqrt[3]{x^-6}\]

Answer 49

sorry, thats messed up looking, but is that right?

Answer 50

Yes it is.

Answer 51

ok. So you can rewrite this as (\[\sqrt[3]{x^6}\]

Answer 52

Without the -6 exponent?

Answer 53

or x^(6/3)

Answer 54

right, because we bring it into the numerator

Answer 55

It makes more sense when you look at everything with fractional exponents rather than radicals

Answer 56

Ohhhhh wow that makes sense! I see now and so if it where x^6/3 wont it be x^2?

Answer 57

because you had 1 / x^(-6/3)

Answer 58

originally

Answer 59

Yeah i see it's a lot easier to see it that way in a fraction.

Answer 60

yeah

Answer 61

So is it x^2?

Answer 62

yep

Answer 63

Thanks man i appreciate it very much

Answer 64

np. thanks for actully trying to learn lol

Answer 65

Haha no problem, better now than never.

Answer 66

wait until you get to logarithms if you think dealing with exponents llke this is confusing

Answer 67

lol

Answer 68

thanks a lot. good luck