How do you simplify ( a^-2/a^5 )^-1?

May 2, 2018

${a}^{7}$

Explanation:

any number to the power of $- 1$ is the same as $1$ divided by that number.

in other words, ${a}^{-} 1 = \frac{1}{a} ^ 1$.

here we have ${a}^{-} \frac{2}{a} ^ 5$

dividing $1$ by ${a}^{-} \frac{2}{a} ^ 5$ gives ${a}^{5} / {a}^{-} 2$.

it is also true that dividing one expression by another with the same base gives the base with a subtracted exponent.

in other words, $\frac{{a}^{m}}{{a}^{n}} = {a}^{m - n}$.

this means that ${a}^{5} / {a}^{-} 2$ is the same as ${a}^{5 - \left(- 2\right)}$

$= {a}^{5 + 2}$

$= {a}^{7}$

hence, ${\left(\frac{{a}^{-} 2}{{a}^{5}}\right)}^{-} 1 = {a}^{5} / {a}^{-} 2 = {a}^{7}$.