# Math Help - Negative fraction powers

1. ## Negative fraction powers

Evaluate 1000^ -2/3

Evaluate 1000^ -2/3
$1000^{\frac{-2}{3}}$

$= \sqrt[3]{1000^{-2}}$

$= 10^{-2}$

$= \frac{1}{100}$

I must assume you know the necessary basics . . .

Evaluate: . $1000^{-\frac{2}{3}}$

We have: . $1000^{-\frac{2}{3}} \;=\;\frac{1}{1000^{\frac{2}{3}}}$

Since $1000 \,=\,10^3$, the denominator is: . $\left(10^3\right)^{\frac{2}{3}} \:=\:10^{(3\cdot\frac{2}{3})}\:=\:10^2\:=\:100$

Answer: . $\frac{1}{100}$