First, we need to understand the following exponent rule:
(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))(xa)b=xa×b
The reverse is also true:
x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)xa×b=(xa)b
We can modify this expression as follows using these rules:
100^(-3/2) = 100^(color(red)(1/2) xx color(blue)(-3)) = (100^(1/2))^-3100−32=10012×−3=(10012)−3
We can now simplify the term within parenthesis:
(100^(1/2))^-3 = 10^-3(10012)−3=10−3
Next we need to understand this rule for exponents:
x^color(red)(a) = 1/x^color(red)(-a)xa=1x−a
Applying this rule to our problem gives:
10^color(red)(-3) = 1/10^color(red)(- -3) = 1/10^color(red)(3) = 1/(10 xx 10 xx 10) = 1/100010−3=110−−3=1103=110×10×10=11000 or 0.0010.001