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

Question

1567 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-26T12:10:43

See the solution process below:

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#

Answer 2 · 2017-04-26T12:32:44

#-2#

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)#