Question

How do you simplify `8^(4/3)`?

Answer 1

`16`

Explanation:

There is an intuitive approach to problems like this.

When an exponent is in the form `a/b`, I do the following in my head:

What is the number to the `1/b` root?

In this case, I'd ask, what is `8` to the `1/3` root? This can also be interpreted as, what is the cube root of `8`?

I know that `2^3=8`, so the cube root of `8` is `2`.

The next step is taking `2` to the `a` power, and here `a=4`.

`2^4=16`, so `8^(4/3)=16`.

Answer 2

`16`

Explanation:

The more formal way to approach this problem is to use the rule `(a^b)^c=a^(bc)` and to rewrite `8` in its prime factorization.

The "simplest" form of `8` is given by `8=2*2*2=2^3`.

Then,

`8^(4/3)=(2^3)^(4/3)=2^(3*4/3)=2^4=16`