How do you simplify q^-3divq^8q3÷q8?

1 Answer
Jan 3, 2017

See full simplification process below

Explanation:

First, we can rewrite this as:

q^-3/q^8q3q8

Now we can simplify using rules for exponents in two ways:

Simplification 1)

Use the rule: x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a) - color(blue)(b))xaxb=xab

q^color(red)(-3)/q^color(blue)(8) = q^(color(red)(-3) - color(blue)(8)) =q3q8=q38=

q^-11q11

Simplification 2)

Use the rule: x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b) - color(red)(a))xaxb=1xba

q^color(red)(-3)/q^color(blue)(8) = 1/q^(color(blue)(8) - color(red)(-3)) = q3q8=1q83=

1/q^111q11