Can you answer and explain this math question please???

Question

Express in simplest radical form

6^(5/3)*a^)2/3)*n^(11/3)
It would be great if you could help me out!! I used to know how to do this when I took the course a few years ago...but for my math class we have to do a review packet and now I have no idea what to do!! Please answer soon!!

Answer 1

Assume question is:-
6^(5/3) a^(2/3) n^(11/3)
[ (6^5) (a²) (n^11) ]^(1/3)
[6² 6³ a² n² n^9 ]^(1/3)
[(6 a n)² (6³) (n^9)]^(1/3)
6 n³ [ (6 a n)² ]^(1/3)
6 n³ [36 a² n² ]^(1/3)
6 n³ (36)^(1/3) a^(2/3) n^(2/3)
6 n^(11/3)(36)^(1/3) a^(2/3)
6 (36)^(1/3) n^(11/3) a^(2/3)
6 [36 n^(11) a² ]^(1/3)

Answer 2

Okay

6^(5/3) * a^(2/3) * n^(11/3)

So first we break up the exponents into
6^[5*(1/3)] * a^[2*(1/3)] __ * n^[11*(1/3)]
And we know that a^(1/b) = b/ a
__
( 2/ a <---- that is the square root of a)
__ __ __
so it is (3/ 6 )^5 * (3/ a )^2 * (3/ n )^11

now we see the radicals are all the 3rd degree. Multiply all the radicand's.

We also know that when multiplying two expressions with exponents together we multiply them.

so we get
__ __ __
(3/ 6 )^5 * (3/ a )^2 * (3/ n )^11
_____
(3/ 6*a*n )^110

since 3 doesnt' go into 110 we cant simplify more.

xD

Answer 3

You have 2 open parenthesis and 4 close parenthesis, so I'll guess that what you are asking is this:

6^(5/3) * a^(2/3) * n^(11/3)

all 3 have 1/3 in the power, so we can take that out right off the bat and get

(6^5 * a^2 * n^11)^1/3

Answer 4

6^(5/3)*a^)2/3)*n^(11/3) Assuming there was a slight typo and that this should read 6^(5/3)*a^(2/3)*n^(11/3), the following can be done

Using the multiplication property of exponents that states exponents are added when mutiplying provided the bases are the same and the fact that 1+(2/3)= (5/3) and 3+(2/3)= (11/3) we have

6*6^(2/3)a^(2/3)n^3*n^(2/3)

Note that all the exponents have the same denominator

Using the definition of rational exponents x^(m/n) = the nth root of x^m 6*6^(2/3)a^(2/3)*n^3*n^(2/3) becomes

6*n^3*the cube root of (6^2a^2n^2) or

6*n^3*the cube root of (36a^2n^2)

Answer 5

6^(5/3) = 6^(3/3)*6^(2/3) = 6*6^(2/3)
n^(11/3) = n^(9/3)*n^(2/3) = n^3*n(2/3)

6*6^(2/3)*a^(2/3)*n^3*n^(2/3)

6n^3(6an)^(2/3)

Answer 6

6n^3(cube root 6^2 * cube root a^2 * cube root n^2)

6n^3 (cube root [36a^2n^2])

Answer 7

notation is too messed up