Question

Simplify the expression

Answer 1

\[\sqrt[4]{16a^2b^6c^4}\]

Answer 2

@mathmale

Answer 3

@Jaynator495

Answer 4

that is the fourth root right?

Answer 5

so first we can write it as \[\sqrt[4]{2^4a^2b^6c^4}\] as a first step
then to write in simplest radical form, note that the index and each term exponent in the radicand are even, so the next good step would be to divide all by 2

Answer 6

okay so \[\sqrt{1^4a^2b^6c^4}\]

Answer 7

?

Answer 8

no

Answer 9

divide each exponent by 2

Answer 10

oh okay

Answer 11

there is going to be another step after that but lets take care of that first

Answer 12

\[^2\sqrt{2^2ab^3c^2}\]

Answer 13

yes good

Answer 14

now is it clear that \(\sqrt{2^2}=2\)?

Answer 15

yeah

Answer 16

this is where you say "yes, that is obvious"

Answer 17

because 2^2=4 then the sqrt of 4 is 2

Answer 18

ok good

Answer 19

how about \(\sqrt{c^2}\)?

Answer 20

wouldn't it still be c?

Answer 21

yes

Answer 22

so the \(2\) comes out of the radical, also the \(c\) comes out of the radical
we have now \[2c\sqrt{ab^3}\] but we are not done yet

Answer 23

because the exponent of \(b\) is 3, and 3 is bigger than the index (which is 2) so we do this:
2 goes in to 2 one time with a remainder of 1, so a \(b^1\) comes out and a \(b^1\) stays in

Answer 24

actually i meant to write "2 goes in to 3 one time, with a remainder of 1"

Answer 25

final answer \[2bc\sqrt{ab}\]

Answer 26

Okay ty

Answer 27

yw

Answer 28

Were you been all day my friend lol