How do you simplify $q^{- 3} \div q^{8}$ $q^-3divq^8$ ?

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Answer 1 · 2017-01-03T00:58:29

See full simplification process below

First, we can rewrite this as:

$\frac{q^{- 3}}{q^{8}}$ $q^-3/q^8$

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

Simplification 1)

Use the rule: $\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a) - color(blue)(b))$

$\frac{q^{- 3}}{q^{8}} = q^{- 3 - 8} =$ $q^color(red)(-3)/q^color(blue)(8) = q^(color(red)(-3) - color(blue)(8)) =$

$q^{- 11}$ $q^-11$

Simplification 2)

Use the rule: $\frac{x^{a}}{x^{b}} = \frac{1}{x^{b - a}}$ $x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b) - color(red)(a))$

$\frac{q^{- 3}}{q^{8}} = \frac{1}{q^{8 - - 3}} =$ $q^color(red)(-3)/q^color(blue)(8) = 1/q^(color(blue)(8) - color(red)(-3)) =$

$\frac{1}{q^{11}}$ $1/q^11$

How do you simplify q−3÷q8q^-3divq^8?