Negative Indices
Simplify the following, giving your answers in negitive indices only.
Example 1
$$ x^4 ÷ x^7$$
Solution
$$ \because a^m ÷ a^n = a^{m-n} $$
$$ \therefore x^4 × x^7 $$
$$ = x^{4-7} $$
$$ = x^{-3} $$
Example 2
$$ b^5 × b^3 $$
Solution
$$ \because a^m × a^n = a^{m+n} \; \textup{and} \; a^n = \frac{1}{a^{-n}}$$
$$ \therefore b^5 × b^3 $$
$$ = b^{5+3} $$
$$ = b^{8} $$
$$ = \frac{1}{b^{-8}} $$
Example 3
$$ c^7 ÷ c^2 $$
Solution
$$ \because a^m ÷ a^n = a^{m-n} \; \textup{and} \; a^n = \frac{1}{a^{-n}}$$
$$ \therefore c^7 ÷ c^2 $$
$$ = c^{7-2} $$
$$ = c^5 $$
$$ = \frac {1}{c^{-5}} $$