How do you simplify 100^(-3/2)10032?

1 Answer
Jan 3, 2017

See full explanation below:

Explanation:

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))^-310032=10012×3=(10012)3

We can now simplify the term within parenthesis:

(100^(1/2))^-3 = 10^-3(10012)3=103

Next we need to understand this rule for exponents:

x^color(red)(a) = 1/x^color(red)(-a)xa=1xa

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) = 1/1000103=1103=1103=110×10×10=11000 or 0.0010.001