Question

(x-79)^(2/5)=64

I have one solution which is 32847 but apparently there is more than one. Help please!

Answer 1

when you take the 5/2 root of 64, you should end up with both positive and negative root

Answer 2

What do you mean by that

Answer 3

x-79=64^(5/2)
=+-32768
so
x=32847 or -32689

When you take a square root you end up with +-.

Answer 4

oooooo okay so you have to plug it back in after that makes sense now

Answer 5

I have another question also

Answer 6

yes

Answer 7

Yeah I still don't really understand how to get those answers haha

Answer 8

I mean:

\[\huge \color{blue}{(\sqrt{64})^5}\]

Answer 9

@OOOPS , you are interpreting 5/2 as 2/5 there..

Answer 10

too much interference. I cannot provide a cogent answer.

Answer 11

Thanks @waterineyes for assistance.

Answer 12

Can I have all of your help on another question too? I've tried this one countless times and cannot seem to find an answer

Answer 13

\[\huge \sqrt[5] {64^2} \ne (64)^{\frac{5}{2}}\]

Answer 14

The perimeter of a rectangle is 200 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 900 feet.

ANSWER: The length (in feet) of a side is in the interval ___ or in the interval ____

Answer 15

ok @oops

Answer 16

@OOOPS you are not at all interfering, thing is you are interpreting 5/2 as 2/5. and this way you are marching towards wrong path, Hope you understand what you are interpreting wrong..

@DominicNg is correct in his explanation..

Answer 17

@emmyvirkus please ask as a new question.

Answer 18

If you like me to explain further why there are 2 answers I can.

Answer 19

Okay please do!

Answer 20

\[(x-79)^\frac{ 2 }{ 5 }=64\]so\[(x-79)^\frac{ 1 }{ 5 }=\sqrt{64}=\pm8\]

Answer 21

\[x-79=(\pm8)^5\]

Answer 22

I suppose you are ok with the rest

Answer 23

where did you get the square root for 64 from

Answer 24

oh because 1/5 squared is 2/5?

Answer 25

let's take a very simple example
\[x^2=64\]then\[x=\sqrt{64}=\pm8\]ok with that?

Answer 26

Yes you are right

Answer 27

Everything alright now?

Answer 28

so I'm taking the square root of (2/5) and of 64 but how do I know that the square root of 2/5 is 1/5? Because when i put it in my calc it comes out as a funky decimal

Answer 29

or should I just know that by common sense lol

Answer 30

another way of seeing it is\[(x-79)^\frac{ 2 }{ 5 }=[(x-79)^\frac{ 1 }{ 5 }]^2\]

Answer 31

So you square root both sides first

Answer 32

then you raise both sides to the 5th power

Answer 33

I dont understand why you don't just take the reciprical of the exponent from the original equation than just add 79 to each side

Answer 34

is that just not the way to solve this particular kind of problem? because that's how I got my first answer

Answer 35

Yes, that is what I did too. I am explaining why there is a plus and minus sign. This comes about because of the square rooting operation. The square rooting operation is hidden in the 'reciprocal of the power' so my purpose is to highlight it.