SOLUTION: Hi; I wondered if you could help me with these problems. I am getting "tangled up" in all the -neg, and exponents. 1. multiply 6/-5 x -3/4 x (-2) and 2. evaluate (1-2^

Algebra ->  Signed-numbers -> SOLUTION: Hi; I wondered if you could help me with these problems. I am getting "tangled up" in all the -neg, and exponents. 1. multiply 6/-5 x -3/4 x (-2) and 2. evaluate (1-2^      Log On


   

Question 323144: Hi; I wondered if you could help me with these problems. I am getting "tangled up" in all the -neg, and exponents.

1. multiply 6/-5 x -3/4 x (-2)
and
2. evaluate (1-2^3)^2 -4 (-5)

I appreciate your time and help!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A good fact to keep in mind is
a%2F%28-b%29+=+-a%2Fb
%28-a%29%2Fb+=+-a%2Fb, so
6%2F%28-5%29+=+-6%2F5
%28-6%2F5%29%2A%28-3%2F4%29%2A%28-2%29
Notice the general form (-) x (-) x (-)
(-) x (-) = (+), so you have
(+) x (-) = (-)
That takes care of your signs, and you have
%28-6%2F5%29%2A%28-3%2F4%29%2A%28-2%29+=+-%286%2F5+%2A+3%2F4+%2A+2%29
+-%286%2F5+%2A+3%2F4+%2A+2%29+=+-36%2F20
-36%2F20+=+-9%2F5
---------------------------------
%281+-+2%5E3%29%5E2+-+4%2A%28-5%29
A helpful rule is "whenever possible, work from the inside out"
%281+-+2%5E3%29%5E2+-+4%2A%28-5%29+=+%281+-+8%29%5E2+-+4%2A%28-5%29
%28-7%29%5E2+-+4%2A%28-5%29+=+49+-+4%2A%28-5%29
49+-+%28-20%29+=+49+%2B+20
49+%2B+20+=+69
I just used the rule
-a%2A%28-b%29+=+ab