Evaluate 1000^(-5/3)

$1000^{- \frac{5}{3}}$

Step 1

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

$\frac{1}{1000^{\frac{5}{3}}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(10^{3})}^{\frac{5}{3}}}$

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

$\frac{1}{10^{3 (\frac{5}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{10^{3 (\frac{5}{3})}}$

Rewrite the expression.

$\frac{1}{10^{5}}$

Raise $10$ to the power of $5$ .

$\frac{1}{100000}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{100000}$

Decimal Form:

$1 \cdot 10^{- 5}$