How do you solve #z^(-1/4) = 1/3#?

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Answer 1 · 2017-01-18T05:00:10

#z^(-1/4)=1/3 <=> z=81#

#z^(-1/4)=1/3#

#<=># First since #x^(-1)=1/x#, and #x^(ab)=(x^a)^b#

#z^((-1)(1/4))=(z^(1/4))^(-1)=1/z^(1/4)=1/3#

#<=>#

#1=z^(1/4)/3# multiply both sides by #z^(1/4)#

#<=>#

#3=z^(1/4)# multiply both sides by 3

#<=>#

#3^4=(z^(1/4))^4# raise both sides to the power of 4

#<=>#

#3^4=z#

#<=>#

#(3^2)^2=(3^2)(3^2)=9(9)=ul(81=z)#