Answer
$\frac{1}{1000}$
Work Step by Step
In this problem, we can break big numbers down to be able to work with them with more ease. Let us break down the number $100$ to base $10$ raised to the $2nd$ power:
$(10^2)^{-3/2}$
Raising a power to a power means we can multiply the two exponents together, keeping the same base. Let's multiply the exponents together first:
$10^{(2)(-3/2)}$
Multiply to simplify the exponents:
$10^{-6/2}$
Reduce the fraction in the exponent by dividing both numerator and denominator by $2$, the greatest common factor:
$10^{-3}$
We don't like to leave negative exponents. To get rid of the negative exponent, we change it into a positive exponent and use its reciprocal, meaning we take the reciprocal of its positive exponent:
$\frac{1}{10^{3}}$
Raise $10$ to the $3rd$ power to solve:
$\frac{1}{1000}$
