If I am reading the question correctly, when the expoent (or power as you say) is a fraction, the numerator is the number you take the power to and the demonator is the number you take the root of.
For example:
$${{\mathtt{16}}}^{\left({\frac{{\mathtt{11}}}{{\mathtt{2}}}}\right)}$$ is the same as $${\sqrt[{{\mathtt{{\mathtt{2}}}}}]{{{\mathtt{16}}}^{{\mathtt{11}}}}}$$. When you multiply the 16 by 16 11 times you get $${\sqrt[{{\mathtt{{\mathtt{2}}}}}]{{\mathtt{17\,592\,186\,044\,416}}}}$$. When you take the square root of 17,592,186,044,416 you get 4,194,304.
If I am reading the question correctly, when the expoent (or power as you say) is a fraction, the numerator is the number you take the power to and the demonator is the number you take the root of.
For example:
$${{\mathtt{16}}}^{\left({\frac{{\mathtt{11}}}{{\mathtt{2}}}}\right)}$$ is the same as $${\sqrt[{{\mathtt{{\mathtt{2}}}}}]{{{\mathtt{16}}}^{{\mathtt{11}}}}}$$. When you multiply the 16 by 16 11 times you get $${\sqrt[{{\mathtt{{\mathtt{2}}}}}]{{\mathtt{17\,592\,186\,044\,416}}}}$$. When you take the square root of 17,592,186,044,416 you get 4,194,304.