Question

Which equation justifies why ten to the one third power equals the cube root of ten?

Answer 1

For this case we have that by definition of power properties it is fulfilled that:

$a ^ {\frac {m} {n}} = \sqrt [n] {a ^ m}$

So, if we have the following expression:

$10 ^ {\frac {1} {3}}$

Using the mentioned property, we can rewrite it as:

$\sqrt [3] {10 ^ 1} = \sqrt [3] {10}$

Answer:

Using the mentioned power property, it is justified that:

$10 ^ {\frac {1} {3}} = \sqrt [3] {10}$