# How do you determine which is greater (3^5)^4 or 3^10?

May 27, 2018

${\left({3}^{5}\right)}^{4} > {3}^{10}$

#### Explanation:

We want to compare ${\left({3}^{5}\right)}^{4}$ with ${3}^{10}$. To do so, we use the following exponent law:

${\left({a}^{m}\right)}^{n} = {a}^{m n}$

So

${\left({3}^{5}\right)}^{4} = {3}^{20}$

$20 > 10$ hence ${3}^{20} > {3}^{10}$

We note that ${3}^{{5}^{4}} > {\left({3}^{5}\right)}^{4}$ because when evaluating exponent towers, we start from the top.