How do you simplify #(- 2x z ^ { 2} ) ^ { 5}#?

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Answer 1 · 2017-10-15T06:14:29

#-32x^5z^10#

Remember that we can rewrite our expression:

#(-2xz^2)^5=(-1)^5(2)^5(x)^5(z^2)^5#

We can now simplify each piece individually:

#(-1)^5=-1xx-1xx-1xx-1xx-1=-1#

#2^5=2xx2xx2xx2xx2=32#

#x^5=x xx x xx x xx x xx x=x^5#

#(z^2)^5=z^5 xx z^2 xx z^2 xx z^2 xx z^2=z^10#

Bringing it all together, we have

#-1 xx 32 xx x^5 xx z^10=-32x^5z^10#

~~~~~

We can find #(z^2)^5# in a different way, remembering the rule that:

#(x^a)^b=x^(ab)#, and so we could have done:

#(x^2)^5=x^(2xx5)=x^10#