How do you simplify #q^-3divq^8#?

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Answer 1 · 2017-01-03T00:58:29

See full simplification process below

First, we can rewrite this as:

#q^-3/q^8#

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))#

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

#q^-11#

Simplification 2)

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

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

#1/q^11#