How do you write $root4(16^3)$ as a fractional exponent?

Question

2281 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-30T04:39:08

$root(4)(16^3)=8$

As $root(n)a=a^(1/n)$ and $(a^m)^(1/n)=a^((mxx1/n))=a^(m/n)$

$root(4)(16^3)=(16^3)^(1/4)=((2^4)^3)^(1/4)=2^((4xx3)/4)$

= $2^(12/4)=2^3=8$

How do you write root4(16^3)root4(16^3) as a fractional exponent?