Question

How do i solve

X^-4 = 1/16

Answer 1

do you know what \(x^{-4}\) means?

Answer 2

Yea 1/x^4?

Answer 3

correct, so you have:\[
x^{-4}=\frac{1}{16}\\
\frac{1}{x^4}=\frac{1}{16}\]

Answer 4

can you solve now?

Answer 5

So, what do i do from here?

Answer 6

come the two sides of the equation - what can you deduce from that?

Answer 7

1*16=x^4*1?

Answer 8

correct

Answer 9

so you now know:\[x^4=16\]

Answer 10

yea

Answer 11

can you write 16 as 2 to the power of something?

Answer 12

I dont know...

Answer 13

what is the square root of 16?

Answer 14

4?

Answer 15

good, so you know:\[16=4^2\]net, what is the square root of 4?

Answer 16

*next

Answer 17

2

Answer 18

what happened to the "x"

Answer 19

good, so \[4=2^2\]which means:\[16=4^2=(2^2)^2=2^4\]agreed so far?

Answer 20

Yes, but I do not understand why we took out x

Answer 21

now we go back to see that:\[x^4=16=2^4\]

Answer 22

can you /see/ what the answer is now?

Answer 23

2^4

Answer 24

if:\[a^4=b^4\]then we can say that a=b

so, if:\[x^4=2^4\]then x=?

Answer 25

ooh, x = 2

Answer 26

U ROCK

Answer 27

:) there are actually more answers but I am not sure what level of maths you are at

Answer 28

Grade 10

Answer 29

how old is that? I am in the UK so am not familiar with grade 10

Answer 30

for example, have you studied complex numbers yet?

Answer 31

The answer you gave me was enough because we are learning quadratic relations

Answer 32

You probably want to at least include x= -2, since (-2)^4 = 16.

Answer 33

x=-2 is also an answer

Answer 34

SO was the answer 2 or -2?

Answer 35

because:\[(-2)^4=16\]

Answer 36

How would I properly show me work when solving this

Answer 37

when you got to the step:\[x^4=16\]you could proceed as follows:\[
x^4=16\\
x=\sqrt[4]{16}=\pm2\]

Answer 38

Becase I have to show how I removed x

Answer 39

does that make sense?

Answer 40

When I root a number to 4 in my calclulator I get 16?

Answer 41

a number = 16

Answer 42

you are probably entering it incorrectly on your calc

Answer 43

enter 16
then press the square root key
then press the square root key again

this is because the fourth root of a number is the same as taking its square root twice

Answer 44

Im getting 8 now?

Answer 45

hmmm.... all I can say is that you are not using the calc you have correctly

are you aware of the wolframalpha web site?

Answer 46

yea, I was just checking on that

Answer 47

http://www.wolframalpha.com/input/?i=4%E2%88%9A16

Answer 48

still 16...

Answer 49

and √√ gets 8

Answer 50

what you entered there was 4 times the square root of 16

Answer 51

Oh, so what would be the correct way

Answer 52

try this: http://www.wolframalpha.com/input/?i=sqrt%28sqrt%2816%29%29

Answer 53

Thankyou very much, you have taught me so much today

Answer 54

You are just an amazing teacher, thaks for your time

Answer 55

you can also do it like this: http://www.wolframalpha.com/input/?i=16^%281%2F4%29

Answer 56

np my friend - I am glad I was able to help you out. :)

Answer 57

thanks

Answer 58

yw :)

Answer 59

say, the root had to be by 6, then we would do


16^1/6 ?

Answer 60

correct

Answer 61

Thanks

Answer 62

since:\[a^{1/b}=\sqrt[b]{a}\]

Answer 63

that is the general form

Answer 64

If you have time,can I ask another similar question

Answer 65

best to post it as a new question

Answer 66

sure

Answer 67

I will help if I can