# How do you simplify the expression 8a^5(a^-2)^6 div (a^-1)^-3?

Apr 5, 2016

$\frac{8}{a} ^ 10$

#### Explanation:

Recall the following rules of exponents :

${x}^{- n} = \frac{1}{x} ^ n$

${\left({x}^{m}\right)}^{n} = {x}^{m n}$

${x}^{m} \cdot {x}^{n} = {x}^{m + n}$

${x}^{m} / {x}^{n} = {x}^{m - n}$

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Now using these rules in conjunction leads to

$8 {a}^{5} \left({a}^{- 12}\right) \div {a}^{3}$

$= \frac{8}{a} ^ 7 \times \frac{1}{a} ^ 3$

$= \frac{8}{a} ^ 10$