# Evaluate the following?

##### 1 Answer
Oct 26, 2016

$\frac{5}{3}$

#### Explanation:

First find each number as the product of its prime factors.
This is easier than it seems.

$390625$ is divisible by 5. You will discover that

$390625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = {5}^{8}$

$6561$ is divisible by 3. You will discover that

$6561 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = {3}^{8}$

${\left(\frac{390625}{6561}\right)}^{\frac{1}{8}} = {\left({5}^{8} / {3}^{8}\right)}^{\frac{1}{8}}$

Recall: ${x}^{\frac{1}{8}} = \sqrt[8]{x}$

${\left(\frac{390625}{6561}\right)}^{\frac{1}{8}} = {\left({5}^{8} / {3}^{8}\right)}^{\frac{1}{8}} = \sqrt[8]{{5}^{8} / {3}^{8}}$

$= \frac{5}{3}$