Question

@terenzreignz please help with this again.. Something different tho, confused on it. Not sure if you combine like terms or what.

\[\sqrt[6]{27a^9b^6c^3}\]

Simplify the expression.

Answer 1

use the property:\[\Huge \sqrt[k]{a^n}=a^{(n/k)}\]

Answer 2

Confused.. I get what k, a, and n equal, just not too sure of what to after the = sign of what you put... Lol. Sorry, new to this and kind'a not too good with it.. :/

Answer 3

divide the exponents under the radical, by the number of the radical

Answer 4

\[\Huge\sqrt[6]{27a^9b^6c^3}\]
\[\Huge{27^{1/6}~a^{9/6}~b^{6/6}~c^{3/6}}\]
then simplify those fractional exponents, preferably into mixed numerals

Answer 5

Okay, so...

\[27^{1/3}a1^{3/6}b^1c^{1/2}\]

Or am I wrong? >.<

Answer 6

youre on the right track, youve just got to get better skills with fractions :)

9/6 = 3/2 = 1 1/2

6/6 = 1 you got right

3/6 = 1/2 you got right

1/6 does not reduce to 1/3 tho

\[\Huge{27^{1/6}~a^{9/6}~b^{6/6}~c^{3/6}}\]
\[\Huge{27^{1/6}~a^{1~~1/2}~b^{1}~c^{1/2}}\]
that mixed numeral, the reason why we want it is it tells us how to
split up that "a": a^1 and a^(1/2)

it also might be good to know that 27 = 3^6, giving us 3^(6/6)

\[\Huge{3ab~a^{1/2}~c^{1/2}}\]

Answer 7

since the denominator of an exponent is the radical number ... we can rewrite those 1/2s as sqrts if need be

Answer 8

pfft, i got my 27^(1/6) bad didnt i ...

Answer 9

27 = 3^3; giving us 3^(3/6), or 3^(1/2)

Answer 10

Okay, so the final answer would be 3^{1/2} ?

Answer 11

Or do we need to clarify more?

Answer 12

3^(1/2) is only the one factor that I messed up on along the way .... the rest of them are still a part of the solution :/

Answer 13

your setup simplifies to:
\[\Huge{ab~3^{1/2}~a^{1/2}~c^{1/2}}\]

you might want to tuck those 1/2 parts under a radical again to complete the process

Answer 14

What do you mean 'tuck them under a radical again'?

Answer 15

werent you here when we went over the property:\[\Huge \sqrt[k]{a^n}=a^{(n/k)}\]

we can convert a radical to a fractional exponent; and we can also convert a fractional exponent back into a radical. A radical has something underneath it, tucked inside of it, placed within it, crammed betwixt it .... etc.

Answer 16

Oh okay, sorry. Blonde moment xD. Thanks so much :)!

Answer 17

youre welcome. if you want to post your final result, i can chk it for you.

Answer 18

Well, that was the correct answer, did not need simplify further, thanks again so much.