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

2 Answers
Apr 26, 2017

See the solution process below:

Explanation:

First, rewrite this expression as:

(-2)^6/(-2)^5

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

x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b)) and a^color(red)(1) = a

(-2)^color(red)(6)/(-2)^color(blue)(5) = (-2)^(color(red)(6)-color(blue)(5)) = (-2)^color(red)(1) = -2

Apr 26, 2017

-2

Explanation:

Consider (-2)^6 the 6 is even so the answer to this part will be positive.

Consider (-2)^5 the 5 is an odd number so the answer to this part is negative.

Consider the overall: we have ("positive number")/("negative number")

color(brown)("So the final answer will be negative.")

Consider the numbers but without the signs.

(2^6)/(2^5) this is the same as " "(2xx2^5)/(2^5)" "=" "2xx2^5/2^5

But 2^5/2^5=1 giving " "2xx1=2

color(brown)("Combining 'negative' and 2 we have: "-2)