Write the Fraction in Simplest Form (1/1000)^(1/3)

${(\frac{1}{1000})}^{\frac{1}{3}}$

Step 1

Apply the product rule to $\frac{1}{1000}$ .

$\frac{1^{\frac{1}{3}}}{1000^{\frac{1}{3}}}$

Step 2

One to any power is one.

$\frac{1}{1000^{\frac{1}{3}}}$

Step 3

Simplify the denominator.

Rewrite $1000$ as $10^{3}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{1}{10}$