How do you simplify #(-5^5y^4z^-5)^6/(2^-2y^-2z^3)#?

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Answer 1 · 2018-03-19T16:10:26

#(2^2*5^30y^26)/z^33#

Answer with positive exponents.

Start with

#(-5^5 y^4 z^-5)^6 /(2^-2 y^-2 z^3)#

To avoid confusion, rewrite as

#((-1)*5^5 y^4 z^-5)^6 /(2^-2 y^-2 z^3)#

Now apply exponent rule #(a^n)^m=a^(nm)#

#((-1)^6*5^30 y^24 z^-30) /(2^-2 y^-2 z^3)#

Note that #(-1)^6=1# because 6 is even so our expression is now

#(5^30 y^24 z^-30) /(2^-2 y^-2 z^3)#

Using exponent laws we know that #1/2^-2= 2^2/1#

#(2^2*5^30 y^24 z^-30) /(y^-2 z^3)#

Exponent laws also tell us that #y^24/y^-2=y^(24--2)=y^(24+2)=y^26# so we can write

#(2^2*5^30 y^26 z^-30) /z^3#

Finally #z^-30/z^3=1/z^(3--30)=1/z^(3+30)=1/z^33# so the answer is

#(2^2*5^30 y^26) /z^33#