Answer
$10$
Work Step by Step
We want to break down this problem a little to be able to work with it. The number $1000$ can be broken down into a small base raised to a power: $10^3$ whereas the number $100$ can be broken down to $10^2$. Let us rewrite these number:
$\dfrac{(10^3)^{4/3}}{(10^2)^{3/2}}$
Raising a power to a power means we can multiply the two powers or exponents to gether:
$\dfrac{10^{(3)(4/3)}}{10^{(2)(3/2)}}$
Multiply to simplify:
$\dfrac{10^{12/3}}{10^{6/2}}$
Reduce the fraction in the exponents by dividing both numerator and denominator by the greatest common factors:
$\dfrac{10^{4}}{10^{3}}$
When we divide exponents with the same base, we keep the base and just subtract the exponent in the denominator from the exponent in the numerator $\left(\frac{a^m}{a^n}=a^{m-n}\right)$"
$10^{4 - 3}$
Subtract the exponents, keeping the base:
$10^{1}$
Any number raised to the first power is that same number. The exponent is no longer needed:
$10$
