How do you find the quotient (-2)^6div(-2)^5?

Apr 26, 2017

See the solution process below:

Explanation:

First, rewrite this expression as:

${\left(- 2\right)}^{6} / {\left(- 2\right)}^{5}$

Now, use these two rules of exponents to complete the division:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$ and ${a}^{\textcolor{red}{1}} = a$

${\left(- 2\right)}^{\textcolor{red}{6}} / {\left(- 2\right)}^{\textcolor{b l u e}{5}} = {\left(- 2\right)}^{\textcolor{red}{6} - \textcolor{b l u e}{5}} = {\left(- 2\right)}^{\textcolor{red}{1}} = - 2$

Apr 26, 2017

$- 2$

Explanation:

Consider ${\left(- 2\right)}^{6}$ the 6 is even so the answer to this part will be positive.

Consider ${\left(- 2\right)}^{5}$ the 5 is an odd number so the answer to this part is negative.

Consider the overall: we have $\left(\text{positive number")/("negative number}\right)$

$\textcolor{b r o w n}{\text{So the final answer will be negative.}}$

Consider the numbers but without the signs.

$\frac{{2}^{6}}{{2}^{5}}$ this is the same as $\text{ "(2xx2^5)/(2^5)" "=" } 2 \times {2}^{5} / {2}^{5}$

But ${2}^{5} / {2}^{5} = 1$ giving $\text{ } 2 \times 1 = 2$

$\textcolor{b r o w n}{\text{Combining 'negative' and 2 we have: } - 2}$