Question 374185
{{{8^(1&1/3)}}}
Mixed numbers are almost always a pain. I usually recommend that they be converted to improper fractions. It is the same here. So we will start by changing {{{1&1/3}}} to 4/3:
{{{8^(4/3)}}}
If you are still not sure how to simplify this, I recommend writing the exponent in a factored form. In this case, we would rewrite the expression as:
{{{8^(4*(1/3))}}}
Since
{{{8^(4*(1/3)) = (8^4)^(1/3)}}}
which says that we raise 8 to the 4th power and then, because an exponent of 1/3 means cube root, find the cube root of the answer.
Also, since multiplication is Commutative, we are free to change the order:
{{{8^((1/3)*4) = (8^(1/3))^4}}}
which says to find a cube root and then raise to the 4th power.<br>
So, in summary, an exponent of {{{4*(1/3)}}} means we will raise to the 4th power and we will find a cube root <i>and we get to choose the order in which these are done!</i><br>
Since 8 is a perfect cube ({{{8 = 2^3}}}), it seems to me that finding the cube root first will be easier than raising 8 to the 4th power. So here's the problem from start to finish:
{{{8^(1&1/3) = 8^(4/3) = 8^((1/3)*4) = (8^(1/3))^4 = 2^4 = 16}}}<br>
(Note: even if you decide to raise to the 4th power first and then find the cube root, you still end up with 16.)