Which value of b solves the equation?

Question

gabbyalicorn · Answer

attachment

gabbyalicorn · Answer

I'm sorry! I don't want to be a burden on you but, @Luigi0210 could you help me with some more problems, please? :3

luigi0210 · Answer

Oh, that should be simple. Do you know what to do when you encounter a negative exponent?

gabbyalicorn · Answer

Kind of....

luigi0210 · Answer

The rule says, when you have a negative exponent you are allowed to flip it to make it positive. 

Sound familiar?

gabbyalicorn · Answer

I thought thats only with -5-(-5) ? They cancel out.

luigi0210 · Answer

That's a different rule (:

But what I mean, is, let's say you have something like $\Large 5^{-2} $, you are allowed to flip it so that negative 2 is positive again, like so: $\huge \frac{1}{5^2} $ 

And the opposite can be done as well

gabbyalicorn · Answer

Oh, that...I've seen that before...

gabbyalicorn · Answer

But I don't get the B part, tho.

luigi0210 · Answer

B is just a variable, like x, that you have to solve, so let's solve it:

So let's flip everything to make that exponent positive
$\Large \frac{1}{b^3} = 216 $ 

Now, let's get rid of that cube:
$\Large (\frac{1}{b^3})^{1/3}=(216)^{1/3}$ 

Which leaves us with $\Large \frac{1}{b} =  6$ 

make sense so far?

gabbyalicorn · Answer

Somewhat.

luigi0210 · Answer

What are you confused on?

gabbyalicorn · Answer

What's the 1/3 suppose to represent? The exponent. If it is. did u do anything to the 216? (like subtract or divide)

luigi0210 · Answer

Wait, I think I made an error, I wasn't suppose to flip that 1/216. Sorry, it'll just be 
 
$\Large \frac{1}{b}=\frac{1}{216} $ 

And yes, that 1/3 is considered an exponent in this certain problem. 
The 216, I took the cubic root of it along with the 1/b^3

gabbyalicorn · Answer

Okay.

luigi0210 · Answer

$\Large \frac{1}{b^3} =\frac{1}{216} $ 

$\Large (\frac{1}{b^3} )^{1/3} = (\frac{1}{216})^{1/3}$ 

$\Large \frac{1}{b} =\frac{1}{6} $ 

Now flip them: 

$\Large b=6 $ 

Which, if you plug it in, would make the statement true

luigi0210 · Answer

Sorry if I went a bit quick >><

gabbyalicorn · Answer

No worries! :) Is the problem asking what number (b) equals to 216

luigi0210 · Answer

Yes, which is the same as 1/216, which would be 6 with that negative exponent.

gabbyalicorn · Answer

but couldn't we just do 216 ÷ 2 and then we will find out what b equals

luigi0210 · Answer

216/2? That's 108?

gabbyalicorn · Answer

yes, it is.

luigi0210 · Answer

How is that 6? o.O

gabbyalicorn · Answer

oh, b is suppose to equal to 6?

luigi0210 · Answer

Yea, 6^3=216, and 6^{-3} = 1/216

gabbyalicorn · Answer

oooooooooooh! The answer is 6!

luigi0210 · Answer

Yea, I even showed you how to solve it <,<

gabbyalicorn · Answer

:o ^///^ sorry! I just started to get it cX

gabbyalicorn · Answer

Thank you.