How do you simplify #(- \frac { 2 1 x ^ { 8 } y ^ { - 8 } } { 3 z ^ { - 7 } } ) ^ { 4 }#?

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Answer 1 · 2018-03-19T15:19:19

#2401x^32y^-32z^28#

Since #(ab)^n=a^nb^n# and #(a/b)^n=a^n/b^n#, we find that we have:

#(21^4*(x^8)^4*(y^-8)^4)/(3^4*(z^-7)^4)#

Since #21^n=3^n*7^n#, we have:

#(3^4*7^4(x^8)^4*(y^-8)^4)/(3^4*(z^-7)^4)#

#(7^4(x^8)^4*(y^-8)^4)/((z^-7)^4)#

Since #(a^n)^b=a^(nb)#, we have:

#(2401x^32y^(-32))/z^-28#

#2401x^32y^-32z^28#