How do you simplify (4n ) ^ { - 9/ 7}?

1 Answer
Parabola
Dec 9, 2017

(root[7] (4^5xxn^5))/(16n^2)

Explanation:

Remember this rule:
a^(-x/y)=1/(root[y] (a^x))

Therefore,
(4n)^(-9/7)=1/(root[7] ((4n)^9)

We simplify the root.
1/(root[7] ((4n)^9) becomes
1/(root[7] ((4^9xxn^9)) We can take 4^7 and n^7 from the root.
1/(root[7] ((4^9xxn^9)) =>1/(4nroot[7] (4^2xxn^2))
We simplify the denominator.
(1xx4^(5/7)xxn^(5/7))/(4nroot[7] (4^2xxn^2)xx4^(5/7)xxn^(5/7)) =>(4^(5/7)xxn^(5/7))/(4xx4xxnxxn) which is really
(root[7] (4^5xxn^5))/(16n^2)

Related questions
Impact of this question
1243 views around the world
You can reuse this answer
Creative Commons License