Question

How do you simplify `\frac { - 8a ^ { 3} b ^ { 3} } { 16a ^ { 3} b }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`-8/16(a^3/a^3)(b^3/b) => -1/2(1)(b^3/b) => -1/2(b^3/b)`

Now, use these two rules of exponents to simplify the `b` terms:

`a = a^color(blue)(1)` and `x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`-1/2(b^color(red)(3)/b^color(blue)(1)) = -1/2b^(color(red)(3)-color(blue)(1)) = -1/2b^2 = -b^2/2`