Carrying over powers to other side of equation

[chrigela]

Hello all,

I am working on an optimization problem in calculus, and when looking at the answer they have transferred powers from one side of the equation to the other.

They have put:

10r=5120/r^2

They then put:
10r^3=5120

Does it become 3 on the left side because when it comes out from the denominator it is negative, but when it switches sides it becomes positive ?
Thanks in advance!

 

[Deleted member 4993]

Hello all,

I am working on an optimization problem in calculus, and when looking at the answer they have transferred powers from one side of the equation to the other.

They have put:

10r=5120/r^2

You are multiplying both sides by r^2 [assuming r $\displaystyle \ne$ 0]

10r * r^2 = 5120/r^2 * r^2

10r^3=5120


They then put:
10r^3=5120

Does it become 3 on the left side because when it comes out from the denominator it is negative, but when it switches sides it becomes positive ?
Thanks in advance!

.

 

[Bob Brown MSEE]

.

It becomes positive because x^-n = 1/xⁿ

 

[fcabanski]

This is an algebra concept. You can also think of it in these terms:

x = 4/x

Isolate the x on the right side by multiplying both sides by x.

x^2 = 4