Question

5th root (-3)^5

._.

Answer 1

It can be written as the power of a power:
\[\large \sqrt[5]{(-3)^{5}}=((-3)^{5})^\frac{1}{5}\]

Answer 2

Just multiply the indices (5 * (1/5).

Answer 3

HI!!

Answer 4

the fifth root of whatever to the power of five is whatever

Answer 5

\[\huge \sqrt[5]{\diamondsuit^5}=\diamondsuit\]

Answer 6

So if it's the same number it's going to be whatever the inside number is? (I have no clue if that made sense)

Answer 7

@misty1212 Do you think you could help me with another problem?

Answer 8

sure

Answer 9

and yes, it is the same number that is inside, so your answer should be \(-3\)

Answer 10

Cool, um, my next question is a 5th root of -1/32

Answer 11

I don't understand fractions all that well and since I'm new to this whole 5th root, I'm extremely confused about it.

Answer 12

your job is to think of a number that, when raised to the fifth power, is 32

Answer 13

don't think too hard , it is easy to come by
that is not the final answer btw, but that is the first step

Answer 14

if you do not get it, let me know
if you do, say it

Answer 15

So it'd just be multiplying something by itself to get to 32?

Answer 16

yes one number, multiplied by itself five times, to give 32

Answer 17

i will be happy to tell you if you like

Answer 18

Would it be 2? and since it's a negative 32, the answer would be -2?

Answer 19

yes \(2^5=32\) so \(\sqrt[5]{32}=2\) but as i said, we are still not done

Answer 20

you want
\[\sqrt{-\frac{1}{32}}\] which is the same as
\[\frac{\sqrt[5] 1}{\sqrt[5]{-32}}\]

Answer 21

\[\sqrt[5]{1}=1\] and
\[\sqrt[5]{-32}=-2\]

Answer 22

So would it be the 5th root 1 over -2?

Answer 23

no it would just be
\[-\frac{1}{2}\]

Answer 24

not the fifth root, you already took the fifth root

Answer 25

Ohhh, I see now.

Answer 26

ok good !!

Answer 27

Thank you! :)

Answer 28

\[\huge \color\magenta\heartsuit\]