Evaluate 1000^(-4/3)

$1000^{- \frac{4}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{1000^{\frac{4}{3}}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(10^{3})}^{\frac{4}{3}}}$

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

$\frac{1}{10^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{10^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{1}{10^{4}}$

Raise $10$ to the power of $4$ .

$\frac{1}{10000}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10000}$

Decimal Form:

$0.0001$