## gabbyalicorn one year ago Which value of b solves the equation?

1. gabbyalicorn

2. gabbyalicorn

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

3. Luigi0210

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

4. gabbyalicorn

Kind of....

5. Luigi0210

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

6. gabbyalicorn

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

7. Luigi0210

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

8. gabbyalicorn

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

9. gabbyalicorn

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

10. Luigi0210

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?

11. gabbyalicorn

Somewhat.

12. Luigi0210

What are you confused on?

13. gabbyalicorn

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

14. Luigi0210

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

15. gabbyalicorn

Okay.

16. Luigi0210

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

17. Luigi0210

Sorry if I went a bit quick >><

18. gabbyalicorn

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

19. Luigi0210

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

20. gabbyalicorn

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

21. Luigi0210

216/2? That's 108?

22. gabbyalicorn

yes, it is.

23. Luigi0210

How is that 6? o.O

24. gabbyalicorn

oh, b is suppose to equal to 6?

25. Luigi0210

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

26. gabbyalicorn

27. Luigi0210

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

28. gabbyalicorn

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

29. gabbyalicorn

Thank you.