#### Answer

The answer is 10.

#### Work Step by Step

To solve this we know that 1000 divided by 10 is 100, and 100 divided by 10 is 10 and 10 divided by 10 is 1. So we know that 1000 = 10$\times$10$\times$10 = $10^{3}$
$1000^{\frac{1}{3}}$ = $({10^{3}})^{\frac{1}{3}}$ = $10^{3\times\frac{1}{3}}$ = $10^{1}$ = 10
Second way
Another way to solve this would be to use the cube root of 1000 because if the exponent is in the format of $\frac{1}{n}$ , the value of n represents the power on the root.
For example
$10^{\frac{1}{5}}$ = $\sqrt[5] 10$