Solve for k

[elder dove]

I can't seem to figure this equation out. Please help.
(with the steps)

[hearty oxide]

What you tried?

[elder dove]

I've reached this step but idk what to do next

i dont know if it matters if the bases are in parentheses or not

[hearty oxide]

it does and in the last line you can already tell there are no solutions

[torn heart]

^

actually not sure thats true

[hearty oxide]

I see the mistake now yes

[spring flame]

Step 4 is not possible. -2^2 does not equal -4

[hearty oxide]

yes!

[torn heart]

well -2^2 does equal 4

but $(-2^2)^k \neq (-2)^{2k}$

[daring canyon]

hiidostuff

[elder dove]

but -2^2 only equals 4 if -2 is in parentheses

[spring flame]

I would simplify -2^6

[torn heart]

sry here i meant -4

-2^2 is -4

[spring flame]

Sorry. Forgot about that

[torn heart]

but the step i wrote above is the incorrect move

[elder dove]

then whats the correct step

[hearty oxide]

you can tell at least that k must be odd

[torn heart]

do $(-1)^k 4^k = -2^6$

[daring canyon]

hiidostuff

[torn heart]

and the solution becomes very clear

[hearty oxide]

,, (-4)^k = -2^6 = -4^3

[daring canyon]

anti-algebraist 𝔸dωn𝓲²s

[torn heart]

yes

so the only possible answer for k is 3

but we have to check it with the exponent for -1

to see if its valid

and sure enough, it is

[hearty oxide]

well 3 is odd lol

[torn heart]

yeah thats a quick way to know its right

[elder dove]

ohhh

now i got it

[torn heart]

nice

[elder dove]

thx for the help :)

.solved

[gusty flame]

Solved

Post marked as solved by @elder dove.

Use .unsolved if this was a mistake.