How do you simplify #\frac { ( - 2) ^ { 4} \times ( - 2) ^ { 4} } { ( - 2) ^ { 2} }#?

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Answer 1 · 2017-11-17T23:45:35

#64#

Evaluate each expression individually first then simplify:

#((-2)^4*(-2)^4)/(-2)^2=(16*16)/4=256/4=64#

Answer 2 · 2017-11-17T23:45:51

#64#

#((-2)^4 * (-2)^4)/(-2)^2#

One rule that will really help here is that when you do an even exponent (2, 4, 6, etc), you will always have a positive number.

#(-2)^4# is the same thing as #(-2)(-2)(-2)(-2)#, which equals to 16.
#(-2)^2# is the same thing as #(-2)(-2)#, which equals to 4.

So now our expression looks like this:
#(16*16)/4#

4
#(cancel(16)*16)/cancel(4)#
1

So #4*16 = 64#