How do you simplify #(8^-2z^-3y)^-1/(5y^2z^-2)^3(5yz^-2)^-1#?

1 Answer
Apr 14, 2016

Answer:

#64/625 xx z^(11)/ y^8#

Explanation:

Take it one step at a time! break the question down into parts. Solve each part then put it all back together again.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "(8^(-2)z^(-3)y))#

#=>1/8^2xx1/z^3xxy/1 = y/(8^2z^3)#

But the whole thing is: #(8^(-2)z^(-3)y)^(-1)#

So #(y/(8^2z^3))^(-1) color(green)(-> (8^2z^3)/y)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "(5y^2z^(-2))^3)#

#=>(5y^2)/1 xx 1/z^2=(5y^2)/z^2#

But the whole thing is #((5y^2)/z^2)^3#

#=>color(green)((5^3y^6)/z^6)" "# ( divide the whole by this one!)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "(5yz^(-2))^(-1)#

#5yz^(-2) -> (5y)/z^2#

But the whole thing is #((5y)/z^2)^(-1)#

#color(green)(=>(z^2)/(5y))#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Putting at all together")#

#(8^2z^3)/y xx (z^2)/(5y) -:( 5^3y^6)/z^6 #

#(8^2z^3)/y xx (z^2)/(5y) xx (z^6)/(5^3y^6) #

#64/625 xx z^(11)/ y^8#